Abstract
Motivated by the descent equation in string theory, we give a new interpretation for the action of the symmetry charges on the BRST cohomology in terms of what we callthe Gerstenhaber bracket. This bracket is compatible with the graded commutative product in cohomology, and hence gives rise to a new class of examples of what mathematicians call aGerstenhaber algebra. The latter structure was first discussed in the context of Hochschild cohomology theory [11]. Off-shell in the (chiral) BRST complex, all the identities of a Gerstenhaber algebra hold up to homotopy. Applying our theory to thec=1 model, we give a precise conceptual description of the BRST-Gerstenhaber algebra of this model. We are led to a direct connection between the bracket structure here and the anti-bracket formalism in BV theory [29]. We then discuss the bracket in string backgrounds with both the left and the right movers. We suggest that the homotopy Lie algebra arising from our Gerstenhaber bracket is closely related to the HLA recently constructed by Witten-Zwiebach. Finally, we show that our constructions generalize to any topological conformal field theory.
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Communicated by A. Jaffe
Supported by NSF Grant DMS-9008459 and DOE Grant DE-FG0292ER25121
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Lian, B.H., Zuckerman, G.J. New perspectives on the BRST-algebraic structure of string theory. Commun.Math. Phys. 154, 613–646 (1993). https://doi.org/10.1007/BF02102111
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DOI: https://doi.org/10.1007/BF02102111