Grothendieck-Teichm\"uller and Batalin-Vilkovisky

TL;DR

This paper establishes a universal action of the Grothendieck-Teichmüller Lie algebra on quantum BV structures of affine supermanifolds with constant odd symplectic forms, linking deep algebraic structures to quantum geometry.

Contribution

It proves the existence of a universal, homotopy-invariant action of r on quantum BV structures on affine supermanifolds with odd symplectic forms.

Findings

Universal action of r on quantum BV structures

Homotopy invariance of the action

Connection between Grothendieck-Teichmüller algebra and quantum BV theory

Abstract

It is proven that, for any affine supermanifold $M$ equipped with a constant odd symplectic structure, there is a universal action (up to homotopy) of the Grothendieck-Teichm\"uller Lie algebra $\mathfrak{grt}_1$ on the set of quantum BV structures (i. e.\ solutions of the quantum master equation) on $M$.