Queries on string connections between branes

Gene Partlow

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>I have questions relating to Brian Greene\'s new book The Fabric of\nthe Cosmos. Specifically, on pg. 390 he shows examples of brane-\nbrane relationships, including how open strings are stuck by their\nendpoints onto their respective branes. In the figure (13.2 b), he\nshows "strings stretching from one two-brane to another".\n\nIn this case the two separate branes (standing in for 3-brane uni-\nverses) are interconnected by open strings, each having one end-\npoint in one brane and the other endpoint stuck in the second\nbrane. I\'d like to know:\n\n1) What kind of particles would match such brane-connecting open\nstrings...ie: bosons (or fermions?) and specifically of *what* sort?\n\n2) Is there any way in which the string itself, stretching between\nits two endpoints (whether both are in the same brane or not),\ncan be seen as analogous to a particle\'s wavefunction (psi)?\n\n3) Since strings have some tension in them, can this be regarded\nas a \'stringy\' tension existing between two distinct brane universes?\n\n4) At least in principle, can two distinct open strings, each having\none endpoint in brane A and one endpoint in brane B, interact such\nthat their two endpoints in brane B, say, unite and thus the two\ndistinct open strings now become one, whose endpoints now live\nentirely in brane A?\n\nAnd is there somewhere on the net or in a book where I can find\nout more detailed information about this? Either popular or tech-\nnical is ok.\n\nThanks,\nGene\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>I have questions relating to Brian Greene's new book The Fabric of
the Cosmos. Specifically, on pg. 390 he shows examples of brane-
brane relationships, including how open strings are stuck by their
endpoints onto their respective branes. In the figure (13.2 b), he
shows "strings stretching from one two-brane to another".

In this case the two separate branes (standing in for 3-brane [itex]uni-[/itex]
verses) are interconnected by open strings, each having one [itex]end-[/itex]
point in one brane and the other endpoint stuck in the second
brane. I'd like to know:

1) What kind of particles would match such brane-connecting open
strings...ie: bosons (or fermions?) and specifically of *what* sort?

2) Is there any way in which the string itself, stretching between
its two endpoints (whether both are in the same brane or not),
can be seen as analogous to a particle's wavefunction [itex](\psi)[/itex]?

3) Since strings have some tension in them, can this be regarded
as a 'stringy' tension existing between two distinct brane universes?

4) At least in principle, can two distinct open strings, each having
one endpoint in brane A and one endpoint in brane B, interact such
that their two endpoints in brane B, say, unite and thus the two
distinct open strings now become one, whose endpoints now live
entirely in brane A?

And is there somewhere on the net or in a book where I can find
out more detailed information about this? Either popular or tech-
nical is ok.

Thanks,
Gene

Lubos Motl

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Wed, 8 Sep 2004, Gene Partlow wrote:\n\n> 1) What kind of particles would match such brane-connecting open\n> strings...ie: bosons (or fermions?) and specifically of *what* sort?\n\nDear Gene, it is good that you ask about these open strings stretched\nbetween two different D-branes because they are unusual and "stringy"\n\nSuch open strings can correspond both to bosons as well as fermions. In\nfact, such a configuration of two branes can easily preserve some\nsupersymmetry, and supersymmetry guarantees that each boson has a partner\nfermion and vice versa.\n\nIf the two D-branes are parallel, then the possible quantum numbers (spins\nand charges) of the open string vibrations mimic the usual open strings\nwhose end points terminate on the same D-brane. However, the masses are\nhigher - the string stretched between different D-branes also has a\ncontribution to mass that originates from the mass of the the string -\nwhich must be longer.\n\nIf you imagine that the two different D-branes actually sit on top of each\nother, you won\'t be able to distinguish the string stretched between the\nD-brane #1 and the D-brane #2 from the string stretched between #1 and #1,\nfor example. Nevertheless, the open strings remember where they end - and\ntherefore the corresponding fields created by these open strings carry two\n"Chan-Paton indices" - each index remembers the label of the brane where\none of the endpoints sits.\n\nThat\'s great because these open string fields therefore transform as\nmatrices - in other words, they transform in the adjoint representation of\na U(N) group - or an SO(N) or Sp(N) group if you introduce orientifolds\nwhich make the open strings unoriented (the usual U(N) open strings are\noriented).\n\nThis extension of the open string fields into matrices holds not only for\nthe gauge fields - which means that you will find a U(N) gauge theory\ndescribing dynamics of open strings at low energies - but they also extend\nto the scalar fields that can be found among the open string vibrations.\nThis means that the transverse positions of the D-branes actually form a\nmatrix.\n\nIf you take D0-branes (D-particles), for example, it is no longer true\nthat 5 D0-particles are described by 5 vectors X^i_m where i=1...9.\nInstead, they are described by a 5x5 Hermitean matrix X^i_{mn} where\nm,n=1,2,3,4,5 and i=1...9. You can diagonalize the matrix X^i - with\nrespect to the indices m,n - and the five eigenvalues are the closest\nthing to a "five positions of five D-particles" that you can get. But\ndifferent coordinates cannot be diagonalized simultaneously, and therefore\nthe geometry seen by D0-branes is "non-commutative" in some specific\nsense.\n\nThis extension of positions of objects into matrices is important in\nMatrix theory. You can imagine that the matrices are diagonal and the\ndiagonal entries inform you about the positions, while the off-diagonal\nentries vanish. But these off-diagonal entries are exactly your strings\nstretched between different D-branes. They correspond to massive states\n(by the way, the way how they get their mass is an example of the Higgs\nmechanism, and therefore the off-diagonal excitations are W-boson-like).\nThe massive states can usually be integrated out, but if the two D0-branes\napproach each other, these massive off-diagonal excitations become light\nonce again, and they are important for dynamics.\n\nIn this sense the diagonal entries describe the positions, while the\noff-diagonal entries generate interactions between the objects - but the\nfull dynamics admits no such a canonical decomposition.\n\nThe appearance of matrices and U(N) gauge groups is important elsewhere in\nstring theory. Maldacena\'s AdS/CFT correspondence implies that a U(N)\nsupersymmetric gauge theory in 4 dimensions is equivalent to gravity on\nthe five-dimensional anti de Sitter space. Well, it is really a\nten-dimensional string theory on AdS_5 x S^5. This exotic appearance of\nextra dimension(s) - or holography - is only possible because the gauge\ntheory contains a large number of strongly coupled degrees of freedom, and\nit is only possible because of the large number of open strings stretched\nbetween different branes.\n\nAbove, I tried to describe the case of parallel D-branes. But the two\nD-branes do not have to be parallel, and they do not have to have the same\ndimensionality. A general pair of D-branes leads to a rather general\nstringy spectrum, but we often consider some special configurations, for\nexample open strings stretched between D0-branes and D4-branes (which, by\nT-duality, has many analogous configurations, such as D4-D8).\n\nIn this D0-D4 case, the open strings stretched between the D0 and the D4\ntransform in the bifundamental representation of U(N) x U(M) where M,N are\nthe numbers of D0 and D4 respectively. This configuration preserves some\nsupersymmetry, and therefore the open strings must transform as a\nsupermultiplet. But this D0-D4 supermultiplet is not the usual vector\nmultiplet found on D4-D4 or D0-D0, the multiplet that contains the gauge\nfield. Instead, the open string states arising from D0-D4 are the\nhypermultiplets - something whose bosonic massless contents only contains\nspinless particles i.e. scalars.\n\n> 2) Is there any way in which the string itself, stretching between\n> its two endpoints (whether both are in the same brane or not),\n> can be seen as analogous to a particle\'s wavefunction (psi)?\n\nIt can have an analogous shape as the graph of a wavefunction, but they\nare complete different things. The position of the open string X(sigma) as\na function of the coordinate sigma along the string is a classical shape.\nWell, it can be quantized, but then X(sigma) for each sigma is an\nobservable that can have a well-defined value (eigenvalue). On the other\nhand, the wavefunction psi(x) is a probabilistic object. Psi(x) for a\nspecific position "x" is not what we call "observable" in quantum\nmechanics. Well, if you second-quantize, then Psi(x) becomes a field which\nis observable, and then it *is* analogous to X(sigma) - but there are also\nmany other things in physics which are functions of a real variable. ;-)\n\n> 3) Since strings have some tension in them, can this be regarded\n> as a \'stringy\' tension existing between two distinct brane universes?\n\nStrings do have tension, and these stretched strings indeed do represent a\nforce between the two D-branes. Such a force is not enough to initiate a\nmotion of two *infinite* D-branes, whose mass is strictly infinite, but\nyou could imagine that it can "attract" two D-particles, for example. Yes,\nit can happen, but there are two problems with this idea: one of them is\nthat perturbatively this force is not seen at the leading order because\neven the finite D-branes are very heavy - their tension is proportional to\n1/g where g (the string coupling) is very small. The open strings are very\nloose and light compared to the D-branes, and therefore you must make a\nmore precise calculation to see how their small force can act on the heave\nD-branes.\n\nSecond, if you have D-particles, the total number of oriented strings\nwhose beginning (first endpoint) ends on the D-particle must equal to the\ntotal number of the second endpoints, because a total electric charge\nwould create flux tubes that would have nowhere to go.\n\n> 4) At least in principle, can two distinct open strings, each having\n> one endpoint in brane A and one endpoint in brane B, interact such\n> that their two endpoints in brane B, say, unite and thus the two\n> distinct open strings now become one, whose endpoints now live\n> entirely in brane A?\n\nYes, definitely. For example, a cubic interaction Trace(C.D.E) where C,D,E\nare three fields coming from such open strings is exactly able to convert\nD,E - which can be two open strings stretched between A,B and B,A\n(opposite orientation) to C - which is then an open string stretched\nbetween A and A. Such interactions occur all the time. The open string\nending on the same D-brane can also become a closed string.\n\n> And is there somewhere on the net or in a book where I can find\n> out more detailed information about this? Either popular or tech-\n> nical is ok.\n\nOpen the newsgroup\'s website\n\nhttp://schwinger.harvard.edu/~sps/\n\nand in the right lower corner you will find links to various links and\npopular resources. I might recommend you Zwiebach\'s new book "A first\ncourse in string theory" that is appropriate for the beginners although it\nis technical (written for undergrads). It discusses the strings stretched\nbetween D-branes - in fact, it even constructs the Standard Model with the\nright particles in this setup.\n\nThe standard more advanced textbooks are Polchinski\'s "String Theory" -\nPolchinski is really the main father of D-branes, so be sure that this is\ninformation from the very source of these ideas - and Green, Schwarz,\nWitten, which is however not up-to-date in this direction because the\nD-branes were not known when GSW wrote their book; the only open strings\nthey discuss are those that can end anywhere - in modern terms, they are\nstretched between space-filling D9-branes (in type I theory).\n\nSorry for any typos above, if you find any, I don\'t have time to fine-tune\nit.\n\nAll the best\nLubos\n__________________________________________________________ ____________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 8 Sep 2004, Gene Partlow wrote:

> 1) What kind of particles would match such brane-connecting open
> strings...ie: bosons (or fermions?) and specifically of *what* sort?

Dear Gene, it is good that you ask about these open strings stretched
between two different D-branes because they are unusual and "stringy"

Such open strings can correspond both to bosons as well as fermions. In
fact, such a configuration of two branes can easily preserve some
supersymmetry, and supersymmetry guarantees that each boson has a partner
fermion and vice versa.

If the two D-branes are parallel, then the possible quantum numbers (spins
and charges) of the open string vibrations mimic the usual open strings
whose end points terminate on the same D-brane. However, the masses are
higher - the string stretched between different D-branes also has a
contribution to mass that originates from the mass of the the string -
which must be longer.

If you imagine that the two different D-branes actually sit on top of each
other, you won't be able to distinguish the string stretched between the
D-brane #1 and the D-brane #2 from the string stretched between #1 and #1,
for example. Nevertheless, the open strings remember where they end - and
therefore the corresponding fields created by these open strings carry two
"Chan-Paton indices" - each index remembers the label of the brane where
one of the endpoints sits.

That's great because these open string fields therefore transform as
matrices - in other words, they transform in the adjoint representation of
a U(N) group - or an SO(N) or Sp(N) group if you introduce orientifolds
which make the open strings unoriented (the usual U(N) open strings are
oriented).

This extension of the open string fields into matrices holds not only for
the gauge fields - which means that you will find a U(N) gauge theory
describing dynamics of open strings at low energies - but they also extend
to the scalar fields that can be found among the open string vibrations.
This means that the transverse positions of the D-branes actually form a
matrix.

If you take D0-branes (D-particles), for example, it is no longer true
that 5 D0-particles are described by 5 vectors [itex]X^{i_m}[/itex] where i=1...9.
Instead, they are described by a 5x5 Hermitean matrix [itex]X^{i_}{mn}[/itex] where
[itex]m,n=1,2,3,4,5[/itex] and [itex]i=1...9.[/itex] You can diagonalize the matrix [itex]X^i -[/itex] with
respect to the indices m,n - and the five eigenvalues are the closest
thing to a "five positions of five D-particles" that you can get. But
different coordinates cannot be diagonalized simultaneously, and therefore
the geometry seen by D0-branes is "non-commutative" in some specific
sense.

This extension of positions of objects into matrices is important in
Matrix theory. You can imagine that the matrices are diagonal and the
diagonal entries inform you about the positions, while the off-diagonal
entries vanish. But these off-diagonal entries are exactly your strings
stretched between different D-branes. They correspond to massive states
(by the way, the way how they get their mass is an example of the Higgs
mechanism, and therefore the off-diagonal excitations are W-boson-like).
The massive states can usually be integrated out, but if the two D0-branes
approach each other, these massive off-diagonal excitations become light
once again, and they are important for dynamics.

In this sense the diagonal entries describe the positions, while the
off-diagonal entries generate interactions between the objects - but the
full dynamics admits no such a canonical decomposition.

The appearance of matrices and U(N) gauge groups is important elsewhere in
string theory. Maldacena's [itex]AdS/CFT[/itex] correspondence implies that a U(N)
supersymmetric gauge theory in 4 dimensions is equivalent to gravity on
the five-dimensional anti de Sitter space. Well, it is really a
ten-dimensional string theory on [itex]AdS_5 x S^5[/itex]. This exotic appearance of
extra dimension(s) - or holography - is only possible because the gauge
theory contains a large number of strongly coupled degrees of freedom, and
it is only possible because of the large number of open strings stretched
between different branes.

Above, I tried to describe the case of parallel D-branes. But the two
D-branes do not have to be parallel, and they do not have to have the same
dimensionality. A general pair of D-branes leads to a rather general
stringy spectrum, but we often consider some special configurations, for
example open strings stretched between D0-branes and D4-branes (which, by
T-duality, has many analogous configurations, such [itex]as D4-D8)[/itex].

In this [itex]D0-D4[/itex] case, the open strings stretched between the D0 and the D4
transform in the bifundamental representation of U(N) x U(M) where M,N are
the numbers of D0 and D4 respectively. This configuration preserves some
supersymmetry, and therefore the open strings must transform as a
supermultiplet. But this [itex]D0-D4[/itex] supermultiplet is not the usual vector
multiplet found on [itex]D4-D4[/itex] or [itex]D0-D0,[/itex] the multiplet that contains the gauge
field. Instead, the open string states arising from [itex]D0-D4[/itex] are the
hypermultiplets - something whose bosonic massless contents only contains
spinless particles i.e. scalars.

> 2) Is there any way in which the string itself, stretching between
> its two endpoints (whether both are in the same brane or not),
> can be seen as analogous to a particle's wavefunction [itex](\psi)[/itex]?

It can have an analogous shape as the graph of a wavefunction, but they
are complete different things. The position of the open string [itex]X(\sigma)[/itex] as
a function of the coordinate [itex]\sigma[/itex] along the string is a classical shape.
Well, it can be quantized, but then [itex]X(\sigma)[/itex] for each [itex]\sigma[/itex] is an
observable that can have a well-defined value (eigenvalue). On the other
hand, the wavefunction [itex]\psi(x)[/itex] is a probabilistic object[itex]. \Psi(x)[/itex] for a
specific position "x" is not what we call "observable" in quantum
mechanics. Well, if you second-quantize, then [itex]\Psi(x)[/itex] becomes a field which
is observable, and then [itex]it *is*[/itex] analogous to [itex]X(\sigma) -[/itex] but there are also
many other things in physics which are functions of a real variable. ;-)

> 3) Since strings have some tension in them, can this be regarded
> as a 'stringy' tension existing between two distinct brane universes?

Strings do have tension, and these stretched strings indeed do represent a
force between the two D-branes. Such a force is not enough to initiate a
motion of two *infinite* D-branes, whose mass is strictly infinite, but
you could imagine that it can "attract" two D-particles, for example. Yes,
it can happen, but there are two problems with this idea: one of them is
that perturbatively this force is not seen at the leading order because
even the finite D-branes are very heavy - their tension is proportional to
1/g where g (the string coupling) is very small. The open strings are very
loose and light compared to the D-branes, and therefore you must make a
more precise calculation to see how their small force can act on the heave
D-branes.

Second, if you have D-particles, the total number of oriented strings
whose beginning (first endpoint) ends on the D-particle must equal to the
total number of the second endpoints, because a total electric charge
would create flux tubes that would have nowhere to go.

> 4) At least in principle, can two distinct open strings, each having
> one endpoint in brane A and one endpoint in brane B, interact such
> that their two endpoints in brane B, say, unite and thus the two
> distinct open strings now become one, whose endpoints now live
> entirely in brane A?

Yes, definitely. For example, a cubic interaction Trace(C.D.E) where C,D,E
are three fields coming from such open strings is exactly able to convert
D,E - which can be two open strings stretched between A,B and B,A
(opposite orientation) to C - which is then an open string stretched
between A and A. Such interactions occur all the time. The open string
ending on the same D-brane can also become a closed string.

> And is there somewhere on the net or in a book where I can find
> out more detailed information about this? Either popular or tech-
> nical is ok.

Open the newsgroup's website

http://schwinger.harvard.edu/~sps/

and in the right lower corner you will find links to various links and
popular resources. I might recommend you Zwiebach's new book "A first
course in string theory" that is appropriate for the beginners although it
is technical (written for undergrads). It discusses the strings stretched
between D-branes - in fact, it even constructs the Standard Model with the
right particles in this setup.

The standard more advanced textbooks are Polchinski's "String Theory" -
Polchinski is really the main father of D-branes, so be sure that this is
information from the very source of these ideas - and Green, Schwarz,
Witten, which is however not up-to-date in this direction because the
D-branes were not known when GSW wrote their book; the only open strings
they discuss are those that can end anywhere - in modern terms, they are
stretched between space-filling D9-branes (in type I theory).

Sorry for any typos above, if you find any, I don't have time to fine-tune
it.

All the best
Lubos
__{____________________________________________________________________ ________}
E-mail: lumo@matfyz.cz fax: [itex]+1-617/496-0110[/itex] Web: http://lumo.matfyz.cz/
eFax: [itex]+1-801/454-1858[/itex] work: [itex]+1-617/384-9488[/itex] home: [itex]+1-617/868-4487[/itex] (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^

Gene Partlow

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0409080944510.10789-100000@feynman.harvard.edu>...\n\n> If you imagine that the two different D-branes actually sit on top of each\n> other, you won\'t be able to distinguish the string stretched between the\n> D-brane #1 and the D-brane #2 from the string stretched between #1 and #1,\n> for example.\n\nHi Lubos,\nI don\'t know if you just mean difficult to distinguish or impossible to\ndistinguish.\n\n[Moderator\'s note: I forgot to include the word "geometrically" in the\nsentence. Sorry. LM]\n\nIf the latter, would it be safe to say that under certain\nspecial circumstances, a local subset of open strings, all on the\n*same* brane A, might become so dense and oriented that they\ninteract with one another to form a second and essentially inde-\npendent brane B (\'sitting right on top of\' the local region of brane\nA? And if so, would all (or some) of the original open strings now\nbecome interbrane strings, stretched between the old and the\nnew branes? See my reference to black holes below (and I apo-\nlogize for this flight of conjecture.)\n\n[Moderator\'s note: The stringy endpoints sort of remember which branes\nthey end on, even if the branes coincide. If you label the different\nbranes by colors, the endpoints of open strings behave as quarks and\nantiquarks with these colors, and an green quark can always annihilate\nwith an antigreen antiquark. If you just want to produce strings\nstretched between different branes from branes stretched between the\nsame branes only, you can simply revert your previous process and\ngenerate the string between #1 and #2 and the "antistring" between\n#2 and #1 in pairs. LM]\n\n> Above, I tried to describe the case of parallel D-branes. But the two\n> D-branes do not have to be parallel, and they do not have to have the same\n> dimensionality.\n\nA key question for me here is What happens if two higher branes (say\n4-branes for sake of discussion) happen to intersect...either two\nplanar branes, being nonparallel...or two spherical branes? My\nmotivation for asking involves a toy model which, Hawking\'s re-\ncent retraction notwithstanding, posits that every black hole may\nforge a permanent link to a separate, unique baby universe brane,\nwhich proceeds to expand in its own frame \'outside\' of our brane.\n[While this model arguably gives a possible source of \'dark matter\'\ngravitational potential leaking back into our universe, from the\nyounger universes, I refrain from details here.]\n\n[Moderator\'s note: I guess that Hawking would call the intersecting\nbrane an object embedded in the same Universe - baby Universes\nrequire the whole spacetime to have nontrivial topology or be\ndisconnected, not just the branes in it. Let me summarize - I don\'t think\nthat your intuition that intersecting branes are related to baby\nUniverses is correct. I leave the rest for answers to others. LM]\n\nPut simply, one way I model it has our brane being a hypersph-\nerical surface containing, among other things, various black holes.\nEach black hole (BH) is *in* our brane, but centered on any BH\nis a much smaller hyperspherical surface, which is its corres-\nponding baby universe brane. Clearly, this brane surface must\nintersect ours, in a higher dimensional AND M-theoretical sense.\nMy continuing puzzles include:\n\n1) What happens at their intersection (if anything)?\n\n2) What might exist between the BH and the baby brane and\ndoes that also interact with our universe brane (is this one aspect\nof Polchinski\'s wandering psi-waves; see below). I can\'t help won-\ndering if the physics of open strings connecting two branes might\nhelp here. Hence my queries.\n\n> > 2) Is there any way in which the string itself, stretching between\n> > its two endpoints (whether both are in the same brane or not),\n> > can be seen as analogous to a particle\'s wavefunction (psi)?\n>\n> It can have an analogous shape as the graph of a wavefunction, but they\n> are complete different things.\n\nOk, I was shooting from the hip here. :-] A few years ago J.\nPolchinski confirmed my conjecture that while particles them-\nselves are \'stuck\' in their respective branes, their psi wavefunc-\ntions may not be, and they can propagate from one to another\nbrane. I thought that must have interesting implications for par-\nticles living in one brane (say ours) but experiencing the \'ghostly\'\nwavefunctions of identical particles which live in other branes.\nHe told me it was one of the avenues M-theorists were exploring\nthen.\n\n> > 4) At least in principle, can two distinct open strings, each having\n> > one endpoint in brane A and one endpoint in brane B, interact such\n> > that their two endpoints in brane B, say, unite and thus the two\n> > distinct open strings now become one, whose endpoints now live\n> > entirely in brane A?\n>\n> Yes, definitely. For example, a cubic interaction Trace(C.D.E) where C,D,E\n> are three fields coming from such open strings is exactly able to convert\n> D,E - which can be two open strings stretched between A,B and B,A\n> (opposite orientation) to C - which is then an open string stretched\n> between A and A. Such interactions occur all the time. The open string\n> ending on the same D-brane can also become a closed string.\n\nGood...that is what I suspected. Thanks for your time and feedback. I\'ll\ncheck out the other sources you mentioned too.\n\nGene\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0409080944510.10...arvard.edu>...

> If you imagine that the two different D-branes actually sit on top of each
> other, you won't be able to distinguish the string stretched between the
> D-brane #1 and the D-brane #2 from the string stretched between #1 and #1,
> for example.

Hi Lubos,
I don't know if you just mean difficult to distinguish or impossible to
distinguish.

[Moderator's note: I forgot to include the word "geometrically" in the
sentence. Sorry. LM]

If the latter, would it be safe to say that under certain
special circumstances, a local subset of open strings, all on the
*same* brane A, might become so dense and oriented that they
interact with one another to form a second and essentially inde-
pendent brane B ('sitting right on top of' the local region of brane
A? And if so, would all (or some) of the original open strings now
become interbrane strings, stretched between the old and the
new branes? See my reference to black holes below (and [itex]I apo-[/itex]
logize for this flight of conjecture.)

[Moderator's note: The stringy endpoints sort of remember which branes
they end on, even if the branes coincide. If you label the different
branes by colors, the endpoints of open strings behave as quarks and
antiquarks with these colors, and an green quark can always annihilate
with an antigreen antiquark. If you just want to produce strings
stretched between different branes from branes stretched between the
same branes only, you can simply revert your previous process and
generate the string between #1 and #2 and the "antistring" between
#2 and #1 in pairs. LM]

> Above, I tried to describe the case of parallel D-branes. But the two
> D-branes do not have to be parallel, and they do not have to have the same
> dimensionality.

A key question for me here is What happens if two higher branes (say
4-branes for sake of discussion) happen to intersect...either two
planar branes, being nonparallel...or two spherical branes? My
motivation for asking involves a toy model which, Hawking's re-
cent retraction notwithstanding, posits that every black hole may
forge a permanent link to a separate, unique baby universe brane,
which proceeds to expand in its own frame 'outside' of our brane.
[While this model arguably gives a possible source of 'dark matter'
gravitational potential leaking back into our universe, from the
younger universes, I refrain from details here.]

[Moderator's note: I guess that Hawking would call the intersecting
brane an object embedded in the same Universe - baby Universes
require the whole spacetime to have nontrivial topology or be
disconnected, not just the branes in it. Let me summarize - I don't think
that your intuition that intersecting branes are related to baby
Universes is correct. I leave the rest for answers to others. LM]

Put simply, one way I model it has our brane being a hypersph-
erical surface containing, among other things, various black holes.
Each black hole (BH) is *in* our brane, but centered on any BH
is a much smaller hyperspherical surface, which is its corres-
ponding baby universe brane. Clearly, this brane surface must
intersect ours, in a higher dimensional AND M-theoretical sense.
My continuing puzzles include:

1) What happens at their intersection (if anything)?

2) What might exist between the BH and the baby brane and
does that also interact with our universe brane (is this one aspect
of Polchinski's wandering [itex]\psi-waves;[/itex] see below). I can't help [itex]won-[/itex]
dering if the physics of open strings connecting two branes might
help here. Hence my queries.

> > 2) Is there any way in which the string itself, stretching between
> > its two endpoints (whether both are in the same brane or not),
> > can be seen as analogous to a particle's wavefunction [itex](\psi)[/itex]?
>
> It can have an analogous shape as the graph of a wavefunction, but they
> are complete different things.

Ok, I was shooting from the hip here. :-] A few years ago J.
Polchinski confirmed my conjecture that while particles them-
selves are 'stuck' in their respective branes, their [itex]\psi[/itex] wavefunc-
tions may not be, and they can propagate from one to another
brane. I thought that must have interesting implications for [itex]par-[/itex]
ticles living in one brane (say ours) but experiencing the 'ghostly'
wavefunctions of identical particles which live in other branes.
He told me it was one of the avenues M-theorists were exploring
then.

> > 4) At least in principle, can two distinct open strings, each having
> > one endpoint in brane A and one endpoint in brane B, interact such
> > that their two endpoints in brane B, say, unite and thus the two
> > distinct open strings now become one, whose endpoints now live
> > entirely in brane A?
>
> Yes, definitely. For example, a cubic interaction Trace(C.D.E) where C,D,E
> are three fields coming from such open strings is exactly able to convert
> D,E - which can be two open strings stretched between A,B and B,A
> (opposite orientation) to C - which is then an open string stretched
> between A and A. Such interactions occur all the time. The open string
> ending on the same D-brane can also become a closed string.

Good...that is what I suspected. Thanks for your time and feedback. I'll
check out the other sources you mentioned too.

Gene

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