## Queries on string connections between branes

<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">&nbsp;&nbsp;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 $uni-$
verses) are interconnected by open strings, each having one $end-$
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 $(\psi)$?

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
nical is ok.

Thanks,
Gene

 PhysOrg.com physics news on PhysOrg.com >> A quantum simulator for magnetic materials>> Atomic-scale investigations solve key puzzle of LED efficiency>> Error sought & found: State-of-the-art measurement technique optimised


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 $X^{i_m}$ where i=1...9. Instead, they are described by a 5x5 Hermitean matrix $X^{i_}{mn}$ where $m,n=1,2,3,4,5$ and $i=1...9.$ You can diagonalize the matrix $X^i -$ 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 $AdS/CFT$ 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 $AdS_5 x S^5$. 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 $as D4-D8)$. In this $D0-D4$ 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 $D0-D4$ supermultiplet is not the usual vector multiplet found on $D4-D4$ or $D0-D0,$ the multiplet that contains the gauge field. Instead, the open string states arising from $D0-D4$ 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 $(\psi)$? It can have an analogous shape as the graph of a wavefunction, but they are complete different things. The position of the open string $X(\sigma)$ as a function of the coordinate $\sigma$ along the string is a classical shape. Well, it can be quantized, but then $X(\sigma)$ for each $\sigma$ is an observable that can have a well-defined value (eigenvalue). On the other hand, the wavefunction $\psi(x)$ is a probabilistic object$. \Psi(x)$ for a specific position "x" is not what we call "observable" in quantum mechanics. Well, if you second-quantize, then $\Psi(x)$ becomes a field which is observable, and then $it *is*$ analogous to $X(\sigma) -$ 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: $+1-617/496-0110$ Web: http://lumo.matfyz.cz/ eFax: $+1-801/454-1858$ work: $+1-617/384-9488$ home: $+1-617/868-4487$ (call) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^



Lubos Motl wrote in message news:... > 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 $I apo-$ 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 $\psi-waves;$ see below). I can't help $won-$ 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 $(\psi)$? > > 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 $\psi$ wavefunc- tions may not be, and they can propagate from one to another brane. I thought that must have interesting implications for $par-$ 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