Modular operads and the quantum open-closed homotopy algebra

TL;DR

This paper demonstrates that specific string field theory algebras are structured as Feynman transforms of modular operads, linking operadic frameworks with quantum open-closed homotopy algebra and BV master equations.

Contribution

It explicitly describes the operadic structure of algebras in string field theory and connects them with solutions to generalized BV master equations.

Findings

Algebras in string field theory are Feynman transforms of modular operads.

Operadic descriptions correspond to solutions of BV master equations.

Provides an explicit operadic framework for quantum open-closed homotopy algebra.

Abstract

We verify that certain algebras appearing in string field theory are algebras over Feynman transform of modular operads which we describe explicitly. Equivalent description in terms of solutions of generalized BV master equations are explained from the operadic point of view.