Duality of generalized Maxwell theories as an equivalence in derived geometry

TL;DR

This paper develops a non-perturbative, derived geometric framework for generalized Maxwell theories, revealing dualities and charge quantization properties in a unified mathematical setting.

Contribution

It introduces a derived differential geometric approach combining BV formalism and differential cohomology to describe moduli spaces and dualities in generalized Maxwell theories.

Findings

Charge quantization is formulated within the derived geometric framework.

Abelian duality between different Maxwell theories is demonstrated.

The compactification of theories is characterized via sheaf pushforwards.

Abstract

We propose a non-perturbative description of the moduli spaces encoding p-form generalized Maxwell theories in any dimension, using derived differential geometry. Our approach synthesizes the Batalin--Vilkovisky formalism with differential cohomology. Within this framework we formulate Dirac charge quantization and show how such charge-quantized moduli spaces exhibit abelian duality between generalized Maxwell theories of different types. We also describe the compactification of generalized Maxwell theories along closed Riemannian manifolds by computing the pushforward of the underlying sheaves of cochain complexes that model differential cohomology.