On Quantum Obstruction Spaces and Higher Codimension Gauge Theories

TL;DR

This paper explores the quantum obstructions in higher codimension gauge theories using the BV-BFV formalism, linking cohomology, algebraic structures, and the quantum master equation.

Contribution

It introduces a cohomological perspective on quantization obstructions and proposes an algebraic framework for higher codimension theories using $ ext{E}_k$-algebras.

Findings

Obstruction for quantizing codimension 1 theories is given by second cohomology.

Proposes an algebraic approach for codimension $k$ quantizations.

Formulates a higher quantum master equation for these theories.

Abstract

Using the quantum construction of the BV-BFV method for perturbative gauge theories, we show that the obstruction for quantizing a codimension 1 theory is given by the second cohomology group with respect to the boundary BRST charge. Moreover, we give an idea for the algebraic construction of codimension $k$ quantizations in terms of $\mathbb{E}_k$-algebras and higher shifted Poisson structures by formulating a higher version of the quantum master equation.