Duality-Symmetry Enhancement in Maxwell Theory
Shani Meynet, Daniele Migliorati, Raffaele Savelli, Michele Tortora
TL;DR
This work analyzes free Maxwell theory on four-manifolds and shows that under specific topological and geometric conditions the Maxwell partition function factorizes holomorphically, revealing new partial symmetries that act on sublattices of flux and can carry mixed 't Hooft anomalies with gravity. By examining both invertible dualities and their non-invertible generalizations, the authors connect zeros of the partition function to underlying anomalies, including at smooth points in the moduli space via generalized theta functions and Leech lattice constructions. They develop a framework of partial gauging and partial non-invertible dualities, demonstrating how these structures can produce zeros in $Z$ without conventional duality anomalies, and provide concrete examples (e.g., extremal metrics, $E_8$ and Leech lattices) to illustrate the phenomena. The results illuminate a rich interplay between topology, geometry, and generalized symmetries, with potential implications for related theories (like $ ext{N}=4$ Abelian theories and six-dimensional self-dual theories) and for understanding how gravity can constrain duality-like structures in quantum field theories.
Abstract
Free Maxwell theory on general four-manifolds may, under certain conditions on the background geometry, exhibit holomorphic factorization in its partition function. We show that when this occurs, new discrete symmetries emerge at orbifold points of the conformal manifold. These symmetries, which act only on a sublattice of flux configurations, are not associated with standard dualities, yet they may carry 't Hooft anomalies, potentially causing the partition function to vanish even in the absence of apparent pathologies. We further explore their non-invertible extensions and argue that their anomalies can account for zeros of the partition function at smooth points in the moduli space.