The MV formalism for ${\rm IBL}_\infty$- and ${\rm BV}_\infty$-algebras

TL;DR

This paper introduces a new formalism for the Quantum Master Equation and the category of MV-algebras, simplifying homotopical algebra related to oriented surfaces with boundary and providing geometric insights.

Contribution

It develops a novel MV formalism that unifies and simplifies the study of ${ m IBL}_ olinebreak_\infty$- and ${ m BV}_ olinebreak_\infty$-algebras, making the quantum master equation more tractable.

Findings

Introduces a category of MV-algebras encompassing ${ m IBL}_ olinebreak_\infty$- and ${ m L}_ olinebreak_\infty$-algebras

Simplifies homotopical algebra in the context of surfaces with boundary

Provides a geometric interpretation of the formalism

Abstract

We develop a new formalism for the Quantum Master Equation $\Delta e^{S/\hbar} = 0$ and the category of ${\rm IBL}_\infty$-algebras and simplify some homotopical algebra arising in the context of oriented surfaces with boundary. We introduce and study a category of MV-algebras, which, on the one hand, contains such important categories as those of ${\rm IBL}_\infty$-algebras and ${\rm L}_\infty$-algebras, and on the other hand, is homotopically trivial, in particular allowing for a simple solution of the quantum master equation. We also present geometric interpretation of our results.