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

Abstract

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 ${\tilde{B}}^2$ term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang-Mills theory is also obtained.

arXiv comment11 pages, LaTeX

References in corpus (5)

• D=26 and Exact Solution to the Conformal-Gauge Two-Dimensional Quantum Gravity
• Construction of an Identically Nilpotent BRS Charge in the Kato-Ogawa String Theory
• Conformal Anomaly of String Theory in the Harmonic Gauge
• Perturbative or Path-Integral Approach versus Operator-Formalism Approach
• How to Solve Quantum Nonlinear Abelian Gauge Theory in Two Dimension in the Heisenberg Picture

Cited by in corpus (1)

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