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

TL;DR

This paper provides exact solutions to two-dimensional BF and Yang-Mills theories in the light-cone gauge, revealing anomalies in the BRS charge and challenging previous string theory critical dimension arguments.

Contribution

It introduces a straightforward method for solving these theories and analyzes the implications of BRS charge anomalies on string theory dimensions.

Findings

Exact solutions for 2D BF and Yang-Mills theories obtained.

BRS Noether charge exhibits anomaly, affecting string theory arguments.

Critique of previous derivations of the critical dimension D=26.

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