Sigma-models and Homotopy Algebras

TL;DR

This paper explores the connection between homotopy algebras in conformal field theory and geometric structures in sigma models, framing conformal invariance as generalized Maurer-Cartan equations related to Einstein equations.

Contribution

It introduces a formulation of conformal invariance conditions in sigma models as generalized Maurer-Cartan equations, linking algebraic and geometric perspectives.

Findings

Conformal invariance conditions are expressed as generalized Maurer-Cartan equations.

In the quasi-classical limit, these conditions reduce to Einstein equations with additional fields.

The work bridges homotopy algebra structures with geometric formulations in sigma models.

Abstract

We review the relation between homotopy algebras of conformal field theory and geometric structures arising in sigma models. In particular we formulate conformal invariance conditions, which in the quasi-classical limit are Einstein equations with extra fields, as generalized Maurer-Cartan equations.