The Batalin–Vilkovisky (BV) formalism provides a cohomological approach for the study of gauge symmetries: given a gauge theory, by introducing extra (non-existing) fields, we can associate to it two cohomology complexes, the BV and the BRST complex. The relevance of these complexes lies in the fact that their cohomology groups capture interesting physical information on the initial theory. In this talk we describe how both these complexes can be seen as Hochschild complexes of a graded algebra B over a bimodule M. By focusing on U(n)-gauge theories induced by a finite spectral triple on Mn(ℂ), we explain how the pair (B,M) is naturally encoded, respectively, in the BV spectral triple associated to the theory for the BV complex and in its gauge – fixed version for the BRST one. This result further reinforces the idea that the BV construction naturally inserts in the framework provided by non-commutative geometry.
This video was produced by the University of Münster, and forms part of the workshop Non-commutative geometry meets topological recursion.
