arivero
Aug21-04, 12:08 AM
It seems to me that the particle content of string theories is not so arbitrary as sometimes we are told.
If I get it well, there are two basic sources of particle content in the theory. On one side, the compactification of the kaluza-klein background should give place to the force fields of the theory. On other side, the vibrational modes of the string should be the matter content. Is it?
Thus from the 10-dimensional restriction of background we should have a total number of 6 gauge fields, should be? This is independent of the background we choose. It is room enough for U(1)xSU(2), but not for QCD gluons. Thus either I am being too naive, or QCD is got from other aspect of strings, or string theory has already been falsyfied and nobody told me.
The matter content comes from the string itself, and it provides us both the elementary fermions and their SUSY partners, does it? Here it does a bit better, as we can expect to see only the fermions for oscillation modes corresponding to the non-compactifyed dimensions. There are 4 of such dimensions (ie usual space-time), and there are 4 different kinds of elementary fermions. So strings could be scoring here. But there is the issue of the scale of the susy partners, and why do we see only the fermions and no one of the corresponding bosons.
I am right in this view? I have never heard any string theoretist arguing that there are four fermions because there are four non-compactified directions for the string, even thought it seems a very positive argument for the theory.
Yours,
Alejandro
Alejandro
Aug22-04, 01:20 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>arivero <arivero@posta.unizar.es> wrote in message news:<arivero.1bb2q6-100000@physicsforums.com>...\n\n> It seems to me that the particle content of string theories is not so\n> arbitrary as sometimes we are told.\n>\n> If I get it well, there are two basic sources of particle content in\n> the theory. On one side, the compactification of the kaluza-klein\n> background should give place to the force fields of the theory. On\n> other side, the vibrational modes of the string should be the matter\n> content. Is it?\n>\n> [Moderator\'s note: Compactification is able to reduce - or preserve\n> - the spin of the particle we started with in 10/11 dimensions, but\n> it is also able to create new, non-gravitational particles.\n> Both "force" and "matter" particles are represented as vibrational\n> modes of a string. For example, as long as supersymmetry is unbroken,\n> all modes come in pairs - boson+fermion. Fermions has to be considered\n> particles of matter while bosons are usually particles of forces. LM]\n\nOK. It seems you are telling that in the current status of the theory,\nall the particle content, both gauge forces and matter, comes from the\nvibrational modes of the string, while the Kaluza Klein background have\na restricted role, just supporting 10-D "gravity". One felts some\nrichesses are lost here, as Kaluza Klein theory was a pretty source for\nparticle content.\n\n[Moderator\'s note: I hopefully did not say that "the only role of the\nKaluza-Klein background is to support 10D gravity" - this statement does\nnot really sound reasonable. The precise spectrum (and interactions) in\nfour dimensions is reflected by the precise theory we start with as well\nas all properties of the compactification. LM]\n\n> It is room enough for U(1)xSU(2), but not for QCD\n> gluons. Thus either I am being too naive, or QCD is got from other\n> aspect of strings, or string theory has already been falsyfied and\n> nobody told me.\n>\n> [Moderator\'s note: I thought that you re-discovered a piece of logic\n> from the 1980s, but now it makes less sense to me. How did you get\n> the number "6" of gauge fields? Originally I thought that you counted\n> the gauge groups that you can obtain through the Kaluza-Klein mechanism\n> ...]\n\nThat was the point, yes. You have described (moderated?) it very accurately.\n\n> [...\n> the SU(3) of QCD. This is one of the reasons why Green+Schwarz discovery\n> of anomaly cancellation in type I string theory was so exciting; this\n> perturbative string theory has an SO(32) gauge group already in ten\n> dimensions. Even though SO(32) is big enough, it turned out that\n> it can\'t be a realistic gauge group to be broken directly to the Standard\n> Model. Therefore another discovery, the heterotic string, was also\n> important for the "First Superstring Revolution" in the 1980s. Its\n> gauge group in 10 dimensions is E8 x E8 which, as it turned out, leads\n> to realistic GUT or Standard Model physics after a compactification\n> on a Calabi-Yau. The E8 x E8 heterotic string was then understood, at\n> least for 10 years, as *the* way how string theory leads to the real\n> world. ]\n\nI see. I though that the freedom for model building was based in the\nbackground, but it is really based in the way the background affects to\nthe modes of the E8xE8 string.\n\n[Moderator\'s note: the "freedom" in the model building is derived from\ndifferent starting points - type I,IIA,IIB,HE,HO string theory or\nM-theory or F-theory with some branes and fluxes - as well as from the\npossible shape of the hidden dimensions, is not it? LM]\n\n> [...\n> This is such a basic result of string theory that it is covered\n> even in most of the popular articles and books on string theory, and\n> it is not quite clear to me what you *have* seen or read about string\n> theory if this result has avoided you so far.\n> ...]\n\nI am very good avoiding results :-)\n\n> I have never heard any string theoretist\n> arguing that there are four fermions because there are four\n> non-compactified directions for the string, even thought it seems a\n> very positive argument for the theory.\n>\n> [Moderator\'s note: I don\'t know what you\'re saying. It is certainly an\n> elementary confusion that the first chapters of textbooks - or even the\n> popular books such as The Elegant Universe - can clarify for you. LM]\n\nAs I have never seen the compactifying process of the E8xE8 string, I was just\nguessing if the fact of having four non compactified dimensions implies\nto have some special modes for the string, associated to these dimensions.\nSuch thing could be a good point for string theory, if four modes were\nspecially underlined (up, down, electron, neutrino)\n\nYours,\nAlejandro\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>arivero <arivero@posta.unizar.es> wrote in message news:<arivero.1bb2q6-100000@physicsforums.com>...
> It seems to me that the particle content of string theories is not so
> arbitrary as sometimes we are told.
>
> If I get it well, there are two basic sources of particle content in
> the theory. On one side, the compactification of the kaluza-klein
> background should give place to the force fields of the theory. On
> other side, the vibrational modes of the string should be the matter
> content. Is it?
>
> [Moderator's note: Compactification is able to reduce - or preserve
> - the spin of the particle we started with in 10/11 dimensions, but
> it is also able to create new, non-gravitational particles.
> Both "force" and "matter" particles are represented as vibrational
> modes of a string. For example, as long as supersymmetry is unbroken,
> all modes come in pairs - boson+fermion. Fermions has to be considered
> particles of matter while bosons are usually particles of forces. LM]
OK. It seems you are telling that in the current status of the theory,
all the particle content, both gauge forces and matter, comes from the
vibrational modes of the string, while the Kaluza Klein background have
a restricted role, just supporting 10-D "gravity". One felts some
richesses are lost here, as Kaluza Klein theory was a pretty source for
particle content.
[Moderator's note: I hopefully did not say that "the only role of the
Kaluza-Klein background is to support 10D gravity" - this statement does
not really sound reasonable. The precise spectrum (and interactions) in
four dimensions is reflected by the precise theory we start with as well
as all properties of the compactification. LM]
> It is room enough for U(1)xSU(2), but not for QCD
> gluons. Thus either I am being too naive, or QCD is got from other
> aspect of strings, or string theory has already been falsyfied and
> nobody told me.
>
> [Moderator's note: I thought that you re-discovered a piece of logic
> from the 1980s, but now it makes less sense to me. How did you get
> the number "6" of gauge fields? Originally I thought that you counted
> the gauge groups that you can obtain through the Kaluza-Klein mechanism
> ...]
That was the point, yes. You have described (moderated?) it very accurately.
> [...
> the SU(3) of QCD. This is one of the reasons why Green+Schwarz discovery
> of anomaly cancellation in type I string theory was so exciting; this
> perturbative string theory has an SO(32) gauge group already in ten
> dimensions. Even though SO(32) is big enough, it turned out that
> it can't be a realistic gauge group to be broken directly to the Standard
> Model. Therefore another discovery, the heterotic string, was also
> important for the "First Superstring Revolution" in the 1980s. Its
> gauge group in 10 dimensions is E8 x E8 which, as it turned out, leads
> to realistic GUT or Standard Model physics after a compactification
> on a Calabi-Yau. The E8 x E8 heterotic string was then understood, at
> least for 10 years, as *the* way how string theory leads to the real
> world. ]
I see. I though that the freedom for model building was based in the
background, but it is really based in the way the background affects to
the modes of the E8xE8 string.
[Moderator's note: the "freedom" in the model building is derived from
different starting points - type I,IIA,IIB,HE,HO string theory or
M-theory or F-theory with some branes and fluxes - as well as from the
possible shape of the hidden dimensions, is not it? LM]
> [...
> This is such a basic result of string theory that it is covered
> even in most of the popular articles and books on string theory, and
> it is not quite clear to me what you *have* seen or read about string
> theory if this result has avoided you so far.
> ...]
I am very good avoiding results :-)
> I have never heard any string theoretist
> arguing that there are four fermions because there are four
> non-compactified directions for the string, even thought it seems a
> very positive argument for the theory.
>
> [Moderator's note: I don't know what you're saying. It is certainly an
> elementary confusion that the first chapters of textbooks - or even the
> popular books such as The Elegant Universe - can clarify for you. LM]
As I have never seen the compactifying process of the E8xE8 string, I was just
guessing if the fact of having four non compactified dimensions implies
to have some special modes for the string, associated to these dimensions.
Such thing could be a good point for string theory, if four modes were
specially underlined (up, down, electron, neutrino)
Yours,
Alejandro
> [Moderator's note: I hopefully did not say that "the only role of the
> Kaluza-Klein background is to support 10D gravity" - this statement does
> not really sound reasonable. The precise spectrum (and interactions) in
> four dimensions is reflected by the precise theory we start with as well
> as all properties of the compactification. LM]
Yep, the Kaluza Klein modes should somehow appear in the 4D world. Perhaps as
a kind of symmetry breaking mechanism? But in any case, it seems that the
heterotic string does not worry a lot about it. If I understand it well, the
background structure in the heterotic string should produce:
a) usual 4 space-time dimensions
b) extra 6 dimensions needed for consistency of the susy part.
c) extra 16 fictitious dimensions needed for consistency of the boson(ized) part.
And all the gauge structure depends of the compactification of (c), while the
compactification of (b) has no important role, except as you say in the final products.
By the way, the heterosis seems to ask for two different "Einstein" equations. On one
side upon (a)+(b) as a superstring theory, on another upon (a)+(b)+(c) as a bosonic string theory. I hope both conditions are consistent one with other. A funny thing is that being (c) obtained from bosonization of 32 fermionic degrees of freedom, somehow an Einstein equation is imposed upon the fermions. How deeply has this detail been exploited?
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