The strong homotopy structure of BRST reduction

Chiara Esposito, Andreas Kraft and Jonas Schnitzer

Vol. 325 (2023), No. 1, 47–83

DOI: 10.2140/pjm.2023.325.47

Abstract

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.

Keywords

reduction, quantization, BRST, formality

Mathematical Subject Classification

Primary: 53D20, 53D55

Milestones

Received: 2 April 2022

Revised: 17 July 2023

Accepted: 17 July 2023

Published: 3 September 2023