Beta-gamma systems and the deformations of the BRST operator

TL;DR

This paper explores the deformation of the BRST operator in beta-gamma systems, linking logarithmic CFTs, algebraic structures, and gauge theory equations like Yang-Mills, revealing deep algebraic relations.

Contribution

It introduces a novel deformation framework of the BRST complex in beta-gamma systems, connecting algebraic structures to nonlinear gauge field equations.

Findings

Deformation of the BRST operator leads to nonlinear field equations.

Yang-Mills equations are derived from the deformed algebraic structure.

Establishes a relation between Courant-Dorfman algebroids and homotopy algebras.

Abstract

We describe the relation between simple logarithmic CFTs associated with closed and open strings, and their "infinite metric" limits, corresponding to the beta-gamma systems. This relation is studied on the level of the BRST complex: we show that the consideration of metric as a perturbation leads to a certain deformation of the algebraic operations of the Lian-Zuckerman type on the vertex algebra, associated with the beta-gamma systems. The Maurer-Cartan equations corresponding to this deformed structure in the quasiclassical approximation lead to the nonlinear field equations. As an explicit example, we demonstrate, that using this construction, Yang-Mills equations can be derived. This gives rise to a nontrivial relation between the Courant-Dorfman algebroid and homotopy algebras emerging from the gauge theory. We also discuss possible algebraic approach to the study of beta-functions in sigma-models.