Francois Belfort
Oct17-04, 07:19 AM
<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>One aim of string theory is to calculate the fine structure constant, of course.\nIt is probably easier to calculate the corresponding constant at the GUT energy,\nwhere the strength of the weak, strong, and electromagnetic interactions\nhave the same value (about 1/30, it seems).\n\nWhat is the path that string theory suggest in order to calculate the value?\nAnd why did nobody succeed up to now? I guess that everybody knows\nthat the calculation is worth a Nobel prize. So why is it so tough?\n(There are only a few candidate symmetry groups, there is only\none string theory; that makes only a handful of choices?)\n\nFB\n\n[Moderator\'s note: It will be great if someone writes a more complete\nexplanation to this good question - I think it is good. Some papers\nargued that the value should be something - like 1/24 - at the\nfundamental scale, but they were more numerology than physics, it\nseems. To determine these constants, you need to find all the\ncontributions to the potential for your scalar fields, and find the\nminima of the potential. So far this counting seems to be\nvery model-dependent, and one cannot calculate the values completely\nin most models anyway. The most important scalar fields in this\ncounting is the four-dimensional dilaton that determines the stringy\ncoupling constant, which is related to the Yang-Mills coupling constant.\nThe four-dimensional dilaton itself can be a mixture of the\nten-dimensional dilaton and the volume-moduli for the hidden dimensions,\nand so on. It\'s a rather complex task, but my feeling also is that\npeople often don\'t try to discuss the value of the gauge coupling\nwhere it\'s stabilized - nevertheless they usually assume that a full\ncalculation leads to a number of order one.\n\nTo get the Nobel prize, you would probably have to find the correct\nstringy background first, because the result seems model-dependent.\nIf you found the correct model, you could probably calculate everything,\nnot just the GUT gauge coupling. ;-)\n\nConcerning the elementary question in the second part. String theory\nhas no dimensionless non-dynamical adjustable parameters. You can\nshow that the gauge coupling *is* determined by the dilaton and the\nvolume of the extra dimensions (or radions or other fields), and you can\nshow that all these scalar fields are dynamical. Then the question is\nwhether there is a potential for them. If there is no potential for the\nscalar fields, we call the scalar fields "moduli" and all of them are\nequally good. They would lead to new massless scalar particles, and these\nwould cause new long-range forces. Experimentally, it is quite clear\nthat there are no moduli in our Universe, and therefore a realistic\nmodel has a nonzero potential for all of them. This occurs, indeed -\nespecially after SUSY breaking we expect potentials for all scalar\nfields. The value of the scalar field(s) that minimize the potential\nwill be chosen in Nature, and these values of the scalars at the minimum\ndetermine the couplings in 4 dimensions. 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>One aim of string theory is to calculate the fine structure constant, of course.
It is probably easier to calculate the corresponding constant at the GUT energy,
where the strength of the weak, strong, and electromagnetic interactions
have the same value (about 1/30, it seems).
What is the path that string theory suggest in order to calculate the value?
And why did nobody succeed up to now? I guess that everybody knows
that the calculation is worth a Nobel prize. So why is it so tough?
(There are only a few candidate symmetry groups, there is only
one string theory; that makes only a handful of choices?)
FB
[Moderator's note: It will be great if someone writes a more complete
explanation to this good question - I think it is good. Some papers
argued that the value should be something - like 1/24 - at the
fundamental scale, but they were more numerology than physics, it
seems. To determine these constants, you need to find all the
contributions to the potential for your scalar fields, and find the
minima of the potential. So far this counting seems to be
very model-dependent, and one cannot calculate the values completely
in most models anyway. The most important scalar fields in this
counting is the four-dimensional dilaton that determines the stringy
coupling constant, which is related to the Yang-Mills coupling constant.
The four-dimensional dilaton itself can be a mixture of the
ten-dimensional dilaton and the volume-moduli for the hidden dimensions,
and so on. It's a rather complex task, but my feeling also is that
people often don't try to discuss the value of the gauge coupling
where it's stabilized - nevertheless they usually assume that a full
calculation leads to a number of order one.
To get the Nobel prize, you would probably have to find the correct
stringy background first, because the result seems model-dependent.
If you found the correct model, you could probably calculate everything,
not just the GUT gauge coupling. ;-)
Concerning the elementary question in the second part. String theory
has no dimensionless non-dynamical adjustable parameters. You can
show that the gauge coupling *is* determined by the dilaton and the
volume of the extra dimensions (or radions or other fields), and you can
show that all these scalar fields are dynamical. Then the question is
whether there is a potential for them. If there is no potential for the
scalar fields, we call the scalar fields "moduli" and all of them are
equally good. They would lead to new massless scalar particles, and these
would cause new long-range forces. Experimentally, it is quite clear
that there are no moduli in our Universe, and therefore a realistic
model has a nonzero potential for all of them. This occurs, indeed -
especially after SUSY breaking we expect potentials for all scalar
fields. The value of the scalar field(s) that minimize the potential
will be chosen in Nature, and these values of the scalars at the minimum
determine the couplings in 4 dimensions. LM]
It is probably easier to calculate the corresponding constant at the GUT energy,
where the strength of the weak, strong, and electromagnetic interactions
have the same value (about 1/30, it seems).
What is the path that string theory suggest in order to calculate the value?
And why did nobody succeed up to now? I guess that everybody knows
that the calculation is worth a Nobel prize. So why is it so tough?
(There are only a few candidate symmetry groups, there is only
one string theory; that makes only a handful of choices?)
FB
[Moderator's note: It will be great if someone writes a more complete
explanation to this good question - I think it is good. Some papers
argued that the value should be something - like 1/24 - at the
fundamental scale, but they were more numerology than physics, it
seems. To determine these constants, you need to find all the
contributions to the potential for your scalar fields, and find the
minima of the potential. So far this counting seems to be
very model-dependent, and one cannot calculate the values completely
in most models anyway. The most important scalar fields in this
counting is the four-dimensional dilaton that determines the stringy
coupling constant, which is related to the Yang-Mills coupling constant.
The four-dimensional dilaton itself can be a mixture of the
ten-dimensional dilaton and the volume-moduli for the hidden dimensions,
and so on. It's a rather complex task, but my feeling also is that
people often don't try to discuss the value of the gauge coupling
where it's stabilized - nevertheless they usually assume that a full
calculation leads to a number of order one.
To get the Nobel prize, you would probably have to find the correct
stringy background first, because the result seems model-dependent.
If you found the correct model, you could probably calculate everything,
not just the GUT gauge coupling. ;-)
Concerning the elementary question in the second part. String theory
has no dimensionless non-dynamical adjustable parameters. You can
show that the gauge coupling *is* determined by the dilaton and the
volume of the extra dimensions (or radions or other fields), and you can
show that all these scalar fields are dynamical. Then the question is
whether there is a potential for them. If there is no potential for the
scalar fields, we call the scalar fields "moduli" and all of them are
equally good. They would lead to new massless scalar particles, and these
would cause new long-range forces. Experimentally, it is quite clear
that there are no moduli in our Universe, and therefore a realistic
model has a nonzero potential for all of them. This occurs, indeed -
especially after SUSY breaking we expect potentials for all scalar
fields. The value of the scalar field(s) that minimize the potential
will be chosen in Nature, and these values of the scalars at the minimum
determine the couplings in 4 dimensions. LM]