Urs Schreiber
Oct13-04, 02:15 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>As far as I am aware there appear to be two different approaches to the\nissue of letting the string tension tend to zero. They are roughly\ndistinguished by the order in which quantization of the string and the T->0\nlimit are applied.\n\nIn the apparently older approach which goes back to Schild and has been\ndeveloped by Gamboa, Lindstroem and others (references given in the recent\nhep-th/0401159) people write down an action that describes null strings,\ncompute the constraints and try to quantize these. The constraints obtained\nthis way look like those for a continuum of N=2 superparticles mutually\nuncoupled except for the reparameterization constraint:\n\nmass shell: P^2 = 0\nDirac: psi.P = 0\nreparameterization: X\'.P + i psi.psi\'/2 = 0 .\n\n(This is the NSR version, the GS version is similar.)\n\nApparently no coherent picture for how the Hilbert space of this theory\nlooks like has emerged yet.\n\nOn the other hand one can consider the ordinary quantization of the string\nin terms of oscillators alpha_n. When these are regarded as not further\ndepending on the tension the only place where the tension still appears is\nin the relation\n\nalpha_0 = sqrt(2alpha\') p .\n\nThis way alpha_0 is scaled in the T->0 limit with respect to the nonzero\nmodes and one naturally obtains a contraction of the Virasoro algebra. (This\ntogether with a list of references can be found in hep-th/0311257 for\ninstance.) Very nice relations to general results of higher spin theory are\nobtained this way.\n\nIt is remarkable that the constraints and the Hilbert space obtained this\nway are different from (all the versions/proposals of) the first approach,\nas far as I can see.\n\nDoes anyone have any idea about if both of these approaches may be useful in\nsome circumstances? For instance which approach is expected to describe the\ntensionless strings appearing on stacks of 5 branes?\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>As far as I am aware there appear to be two different approaches to the
issue of letting the string tension tend to zero. They are roughly
distinguished by the order in which quantization of the string and the T->0
limit are applied.
In the apparently older approach which goes back to Schild and has been
developed by Gamboa, Lindstroem and others (references given in the recent
http://www.arxiv.org/abs/hep-th/0401159) people write down an action that describes null strings,
compute the constraints and try to quantize these. The constraints obtained
this way look like those for a continuum of N=2 superparticles mutually
uncoupled except for the reparameterization constraint:
mass shell: P^2 =
Dirac: \psi.P =
reparameterization: X'.P + i \psi.\psi'/2 = .
(This is the NSR version, the GS version is similar.)
Apparently no coherent picture for how the Hilbert space of this theory
looks like has emerged yet.
On the other hand one can consider the ordinary quantization of the string
in terms of oscillators \alpha_n. When these are regarded as not further
depending on the tension the only place where the tension still appears is
in the relation
\alpha_0 = \sqrt(2alpha') p .
This way \alpha_0 is scaled in the T->0 limit with respect to the nonzero
modes and one naturally obtains a contraction of the Virasoro algebra. (This
together with a list of references can be found in http://www.arxiv.org/abs/hep-th/0311257 for
instance.) Very nice relations to general results of higher spin theory are
obtained this way.
It is remarkable that the constraints and the Hilbert space obtained this
way are different from (all the versions/proposals of) the first approach,
as far as I can see.
Does anyone have any idea about if both of these approaches may be useful in
some circumstances? For instance which approach is expected to describe the
tensionless strings appearing on stacks of 5 branes?
issue of letting the string tension tend to zero. They are roughly
distinguished by the order in which quantization of the string and the T->0
limit are applied.
In the apparently older approach which goes back to Schild and has been
developed by Gamboa, Lindstroem and others (references given in the recent
http://www.arxiv.org/abs/hep-th/0401159) people write down an action that describes null strings,
compute the constraints and try to quantize these. The constraints obtained
this way look like those for a continuum of N=2 superparticles mutually
uncoupled except for the reparameterization constraint:
mass shell: P^2 =
Dirac: \psi.P =
reparameterization: X'.P + i \psi.\psi'/2 = .
(This is the NSR version, the GS version is similar.)
Apparently no coherent picture for how the Hilbert space of this theory
looks like has emerged yet.
On the other hand one can consider the ordinary quantization of the string
in terms of oscillators \alpha_n. When these are regarded as not further
depending on the tension the only place where the tension still appears is
in the relation
\alpha_0 = \sqrt(2alpha') p .
This way \alpha_0 is scaled in the T->0 limit with respect to the nonzero
modes and one naturally obtains a contraction of the Virasoro algebra. (This
together with a list of references can be found in http://www.arxiv.org/abs/hep-th/0311257 for
instance.) Very nice relations to general results of higher spin theory are
obtained this way.
It is remarkable that the constraints and the Hilbert space obtained this
way are different from (all the versions/proposals of) the first approach,
as far as I can see.
Does anyone have any idea about if both of these approaches may be useful in
some circumstances? For instance which approach is expected to describe the
tensionless strings appearing on stacks of 5 branes?