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

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

2001-11-16

arxiv.org/abs/hep-th/0111148v1

Int.J.Mod.Phys. A17 (2002) 1491-1502

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX

Scientific paper

10.1142/S0217751X02009825

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.

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