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Exact Solutions to the Two-dimensional BF and Yang-Mills Theories in the Light-cone Gauge

Mitsuo Abe, Noboru Nakanishi

Published 2001-11-16Version 1

It is shown that the BRS-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated two-dimensional quantum gravity in the conformal gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a criticism is made on the reasoning of Kato and Ogawa, who derived the critical dimension D=26 of string theory on the basis of the anomaly of the BRS Noether charge. By adding the $\widetilde{B}^2$ term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang-Mills theory is also obtained.

Comments: 11 pages, LaTeX
Journal: Int.J.Mod.Phys. A17 (2002) 1491-1502
Categories: hep-th
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