Scott
Dec5-04, 01:41 PM
<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 a question about the spectrum of particles predicted in string\ntheory. Assuming I have this correct here goes. If I look only at open\nstrings I can predict the particle spectrum and I can get scalars,\nvectors, spinors, maybe spin 3/2, but no spin 2 particles. We can then\nlook at the closed string particle spectrum and the graviton shows up\nalong with the rest.\n\n[Moderator\'s note: You get particles of arbitrary spin, but they\'re\nmassive - with masses comparable to the string scale. Massless particles\nare very constrained by consistency, and your list is essentially\ncomplete and correct. The only meaningful interacting\ntheory of spin 2 particles is a theory with diffeomorphisms - as the\nnonlinear deformation of the spin 2 gauge invariance - in other words,\ngeneral relativity. The gravitons can\'t be carried by open strings\nbecause gravity is, by definition, the geometry of the whole spacetime,\nnot just physics attached to some D-branes. Gravitons are always closed\nstrings if there are any strings at all. LM]\n\nHere is where I get confused. When I calculated this spectrum, I got\nall the particles in the standard model (SM), yet I never included\nexcited modes of the string. When I do look at excited modes of the\nstring the energies are so high we would never see these particles\ntoday correct?\n\n[Moderator\'s note: Assuming the conventional scenarios, the excited\nstrings are hugely massive and they will never be produced. On the other\nhand, the "low energy gravity" models from the\nlate 1990s - large extra dimensions or warped extra dimensions - allow\nthe excited strings to be accessible as early as at the LHC. LM]\n\nIf so, how do we see all the different particles in the SM, if they\nare all represented by a string in its ground state? Does it have to\ndo with the string being constrained to some of the 26 dimensions, or\nhow the space is compactified.\n\n[Moderator\'s note: In the RNS formalism, the massless level is not\nreally the ground state - it is the first excited state above the\ntachyonic ground state; the tachyonic ground state itself is\nprojected out by the GSO projections. Because the massless states\nare really excited, there are many ways how can you get the right\namount of excitation. In the other, Green-Schwarz formalism, the ground\nstate itself is degenerate (it has many states).\nMoreover, as you say correctly, the\nfour-dimensional particles also carry a wave function in the extra\n6 dimensions - and there are several wave functions that protect\nthe vanishing energy. These wave functions are associated with the\ncohomology of the Calabi-Yau internal six-dimensional space.\nConsequently, the number of generations depends on the topology\n- 1/2 of the Euler character - of the six-dimensional manifold. LM]\n\nFor example, an electron and a muon would both be produced by the\nstring in its ground state. So how do I determine which particle is\nwhich in the context of string theory?\n\n[Moderator\'s note: In the conventional models - heterotic strings\nor heterotic M-theory (Horava-Witten M-theory with 2 boundaries) on\nCalabi-Yau spaces - the electron and muon are two Kaluza-Klein\nmodes of the same field in 10 dimensions that differ by a different\ndependence of their wave function on the 6 internal dimensions.\nThere are several "closed differential forms" of the right rank.\nIn the braneworld scenarios, the electron and the muon are excitations\nof fields associated with different branes or their intersections. LM]\n\nI realize this isn\'t completly physical since I didn\'t include SUSY,\nbut I think the concept is the same if we include SUSY and look at\n10d.\n\n[Moderator\'s note: Yes, the main ideas should work the same way with\nSUSY or with SUSY broken - by any means. With unbroken SUSY, there\nare many other physical particles in the same multiplet (selectron,\nsmuon...). LM]\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 a question about the spectrum of particles predicted in string
theory. Assuming I have this correct here goes. If I look only at open
strings I can predict the particle spectrum and I can get scalars,
vectors, spinors, maybe spin 3/2, but no spin 2 particles. We can then
look at the closed string particle spectrum and the graviton shows up
along with the rest.
[Moderator's note: You get particles of arbitrary spin, but they're
massive - with masses comparable to the string scale. Massless particles
are very constrained by consistency, and your list is essentially
complete and correct. The only meaningful interacting
theory of spin 2 particles is a theory with diffeomorphisms - as the
nonlinear deformation of the spin 2 gauge invariance - in other words,
general relativity. The gravitons can't be carried by open strings
because gravity is, by definition, the geometry of the whole spacetime,
not just physics attached to some D-branes. Gravitons are always closed
strings if there are any strings at all. LM]
Here is where I get confused. When I calculated this spectrum, I got
all the particles in the standard model (SM), yet I never included
excited modes of the string. When I do look at excited modes of the
string the energies are so high we would never see these particles
today correct?
[Moderator's note: Assuming the conventional scenarios, the excited
strings are hugely massive and they will never be produced. On the other
hand, the "low energy gravity" models from the
late 1990s - large extra dimensions or warped extra dimensions - allow
the excited strings to be accessible as early as at the LHC. LM]
If so, how do we see all the different particles in the SM, if they
are all represented by a string in its ground state? Does it have to
do with the string being constrained to some of the 26 dimensions, or
how the space is compactified.
[Moderator's note: In the RNS formalism, the massless level is not
really the ground state - it is the first excited state above the
tachyonic ground state; the tachyonic ground state itself is
projected out by the GSO projections. Because the massless states
are really excited, there are many ways how can you get the right
amount of excitation. In the other, Green-Schwarz formalism, the ground
state itself is degenerate (it has many states).
Moreover, as you say correctly, the
four-dimensional particles also carry a wave function in the extra
6 dimensions - and there are several wave functions that protect
the vanishing energy. These wave functions are associated with the
cohomology of the Calabi-Yau internal six-dimensional space.
Consequently, the number of generations depends on the topology
- 1/2 of the Euler character - of the six-dimensional manifold. LM]
For example, an electron and a muon would both be produced by the
string in its ground state. So how do I determine which particle is
which in the context of string theory?
[Moderator's note: In the conventional models - heterotic strings
or heterotic M-theory (Horava-Witten M-theory with 2 boundaries) on
Calabi-Yau spaces - the electron and muon are two Kaluza-Klein
modes of the same field in 10 dimensions that differ by a different
dependence of their wave function on the 6 internal dimensions.
There are several "closed differential forms" of the right rank.
In the braneworld scenarios, the electron and the muon are excitations
of fields associated with different branes or their intersections. LM]
I realize this isn't completly physical since I didn't include SUSY,
but I think the concept is the same if we include SUSY and look at
10d.
[Moderator's note: Yes, the main ideas should work the same way with
SUSY or with SUSY broken - by any means. With unbroken SUSY, there
are many other physical particles in the same multiplet (selectron,
smuon...). LM]
theory. Assuming I have this correct here goes. If I look only at open
strings I can predict the particle spectrum and I can get scalars,
vectors, spinors, maybe spin 3/2, but no spin 2 particles. We can then
look at the closed string particle spectrum and the graviton shows up
along with the rest.
[Moderator's note: You get particles of arbitrary spin, but they're
massive - with masses comparable to the string scale. Massless particles
are very constrained by consistency, and your list is essentially
complete and correct. The only meaningful interacting
theory of spin 2 particles is a theory with diffeomorphisms - as the
nonlinear deformation of the spin 2 gauge invariance - in other words,
general relativity. The gravitons can't be carried by open strings
because gravity is, by definition, the geometry of the whole spacetime,
not just physics attached to some D-branes. Gravitons are always closed
strings if there are any strings at all. LM]
Here is where I get confused. When I calculated this spectrum, I got
all the particles in the standard model (SM), yet I never included
excited modes of the string. When I do look at excited modes of the
string the energies are so high we would never see these particles
today correct?
[Moderator's note: Assuming the conventional scenarios, the excited
strings are hugely massive and they will never be produced. On the other
hand, the "low energy gravity" models from the
late 1990s - large extra dimensions or warped extra dimensions - allow
the excited strings to be accessible as early as at the LHC. LM]
If so, how do we see all the different particles in the SM, if they
are all represented by a string in its ground state? Does it have to
do with the string being constrained to some of the 26 dimensions, or
how the space is compactified.
[Moderator's note: In the RNS formalism, the massless level is not
really the ground state - it is the first excited state above the
tachyonic ground state; the tachyonic ground state itself is
projected out by the GSO projections. Because the massless states
are really excited, there are many ways how can you get the right
amount of excitation. In the other, Green-Schwarz formalism, the ground
state itself is degenerate (it has many states).
Moreover, as you say correctly, the
four-dimensional particles also carry a wave function in the extra
6 dimensions - and there are several wave functions that protect
the vanishing energy. These wave functions are associated with the
cohomology of the Calabi-Yau internal six-dimensional space.
Consequently, the number of generations depends on the topology
- 1/2 of the Euler character - of the six-dimensional manifold. LM]
For example, an electron and a muon would both be produced by the
string in its ground state. So how do I determine which particle is
which in the context of string theory?
[Moderator's note: In the conventional models - heterotic strings
or heterotic M-theory (Horava-Witten M-theory with 2 boundaries) on
Calabi-Yau spaces - the electron and muon are two Kaluza-Klein
modes of the same field in 10 dimensions that differ by a different
dependence of their wave function on the 6 internal dimensions.
There are several "closed differential forms" of the right rank.
In the braneworld scenarios, the electron and the muon are excitations
of fields associated with different branes or their intersections. LM]
I realize this isn't completly physical since I didn't include SUSY,
but I think the concept is the same if we include SUSY and look at
10d.
[Moderator's note: Yes, the main ideas should work the same way with
SUSY or with SUSY broken - by any means. With unbroken SUSY, there
are many other physical particles in the same multiplet (selectron,
smuon...). LM]