From surface roughening to QCD string theory Page: 21 of 23
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not far from gR, in the domain of the critical KT phase, should be essen-
tially identical to Eqs. (4, 5, 6) of our BCSOS spectrum in QCD3. This
spectrum exhibits the features of a two-dimensional conformal field theory
with c=1 conformal charge. In QCD4 we do not expect qualitative changes.
The precise physical interpretation of the spectrum around the roughening
point in terms of a geometric string theory will require further work. This is
facilitated by the observation that the spectrum is equivalent to that of the
two-dimensional Gaussian scalar field on a circle, including defect lines in the
field configurations of the path integral for the partition function.
5.2 Crossover to continuum QCD
Now, is the Kosterlitz-Thouless picture identical to what we expect in con-
tinuum QCD3 string theory? As we have seen, the Wilson surface in QCD3
is in the massless Kosterlitz-Thouless phase for gauge couplings weaker than
the roughening coupling. Based on universality arguments, this alone should
determine the complete low-energy spectrum of the surface. However, as the
coupling weakens below gR and we take the g - 0 continuum limit, an im-
portant question arises. Do we expect a change in the structure of the low
energy spectrum from the KT universality class into something else which
should be identified as the universality class of continuum QCD string the-
ory? This transition from the KT phase to continuum QCD3 string theory
should be particularly intriguing. On one hand, the expected transition is
quite plausible, given the fact that we are sitting at gR in the bulk which is
far from the critical region of the continuum limit. Why would this rough sur-
face look identical to the continuum Wilson surface? On the other hand, the
Wilson surface is unlikely to go back into a massive phase again as we move
towards g = 0. This would require a new critical point g, somewhere between
gR < g, < 0 which is not likely. The only plausible scenario is that the surface
remains massless throughout the gR < g < 0 region and its critical behavior
will cross over from the Kosterlitz-Thouless class into the universality class of
continuum QCD string theory whose precise description remains the subject
of our future investigations.
Acknowledgments
One of us (J. K.) would like to acknowledge valuable discussions with P. Hasen-
fratz, K. Intriligator, F. Niedermayer, J. Polchinski, S. Renn, U.-J. Wiese,
and J.-B. Zuber. J. K. is also thankful to the organizers of the workshop who
created a stimulating atmosphere throughout the meeting. This work wasSubmitted to the World Scientific Conference Proceedings
211
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al., Keisuke Jimmy Juge et. From surface roughening to QCD string theory, article, May 23, 2001; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc723700/m1/21/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.