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It is shown that the BRS-formulated two-dimensional BF theory in thelight-cone gauge (coupled with chiral Dirac fields) is solved very easily inthe Heisenberg picture. The structure of the exact solution is very similar tothat of the BRS-formulated two-dimensional quantum gravity in the conformalgauge. In particular, the BRS Noether charge has anomaly. Based on this fact, acriticism is made on the reasoning of Kato and Ogawa, who derived the criticaldimension D=26 of string theory on the basis of the anomaly of the BRS Noethercharge. By adding the $\widetilde{B}^2$ term to the BF-theory Lagrangiandensity, the exact solution to the two-dimensional Yang-Mills theory is alsoobtained.Comment: 11 pages, LaTe

EXACT SOLUTIONS TO THE TWO-DIMENSIONAL BF AND YANG–MILLS THEORIES IN THE LIGHT-CONE GAUGE