The Strong Homotopy Structure of BRST Reduction

Abstract

In this paper we propose a reduction scheme for polydifferential operators phrased in terms of $L_{\infty }$-morphisms. The desired reduction $L_{\infty }$-morphism has been obtained by applying an explicit version of the homotopy transfer theorem. Finally, we prove that the reduced star product induced by this reduction $L_{\infty }$-morphism and the reduced star product obtained via the formal Koszul complex are equivalent.

27 pages, comments are welcome!