On Quantum Obstruction Spaces and Higher Codimension Gauge 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.