Does the fivebrane have a nonclassical BV-structure?

TL;DR

This paper investigates the BV-quantization of the fivebrane's higher gauge field in M-theory, proposing a nonclassical BV-structure involving a fourth order Master equation and nonlinear algebraic features.

Contribution

It introduces a novel algebraic framework suggesting the BV-structure for fivebrane gauge theories is fundamentally different from classical cases, involving higher order equations.

Findings

A fourth order Master equation is proposed for the fivebrane gauge theory.

A second order term in the Master equation indicates nonlinear algebraic deformation.

Deformation theory here extends beyond traditional complexes and cohomology.

Abstract

The fivebrane in M-theory comes equipped with a higher order gauge field which should have a formulation in terms of a 2-gerbe on the fivebrane. One can pose the question if the BV-quantization scheme for such a higher order gauge theory should differ from the usual BV-algebra structure. We give an algebraic argument that this should, indeed, be the case and a fourth order equation should appear as Master equation, in this case. We also discover a second order term in this equation which seems to indicate that deformation theory (i.e. solving the Master equation) in this case involves a nonlinear algebraic theory which goes beyond complexes and cohomology.