BV and BFV Formulation of a Gauge Theory of Quadratic Lie Algebras in 2-d and a Construction of W3 Topological Gravity
Abstract
The recently proposed generalized field method for solving the master equation of Batalin and Vilkovisky is applied to a gauge theory of quadratic Lie algebras in 2-dimensions. The charge corresponding to BRST symmetry derived from this solution in terms of the phase space variables by using the Noether procedure, and the one found due to the BFV-method are compared and found to coincide. W3 algebra, formulated in terms of a continuous variable is emploied in the mentioned gauge theory to construct a W3 topological gravity. Moreover, its gauge fixing is briefly discussed.
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