DGLA Dg and BV formalism

TL;DR

This paper explores the use of Differential Graded Lie Algebras (Dg) in the context of current algebras and BV formalism, revealing new connections between algebraic structures and string theory vertex operators.

Contribution

It demonstrates how constructing equivariantly closed forms relates to representing Dg, clarifying the link between algebraic models and string theory operators.

Findings

Reduction of equivariant form construction to Dg representation

Clarification of the relation between integrated and unintegrated vertex operators

Extension of BV formalism within the Dg framework

Abstract

Differrential Graded Lie Algebra Dg was previously introduced in the context of current algebras. We show that under some conditions, the problem of constructing equivariantly closed form from closed invariant form is reduces to construction of a representation of Dg. This includes equivariant BV formalism. In particular, an analogue of intertwiner between Weil and Cartan models allows to clarify the general relation between integrated and unintegrated vertex operators in string worldsheet theory.