Phase structure of self-dual lattice gauge theories in 4d

TL;DR

This paper explores the phase structure of 4d self-dual lattice gauge theories with electric and magnetic matter, revealing a rich symmetry group and supporting a specific phase diagram through numerical simulations.

Contribution

It introduces a modified Villain lattice gauge model with electric-magnetic duality, analyzes its self-dual symmetry, and provides numerical evidence for its phase structure.

Findings

Identification of a self-dual symmetry group as a central extension of Z_4

Numerical support for the proposed phase diagram

Characterization of the phase structure in the simplest self-dual case

Abstract

We discuss U(1) lattice gauge theory models based on a modified Villain formulation of the gauge action, which allows coupling to bosonic electric and magnetic matter. The formulation enjoys a duality which maps electric and magnetic sectors into each other. We propose several generalizations of the model and discuss their 't~Hooft anomalies. A particularly interesting class of theories is the one where electric and magnetic matter fields are coupled with identical actions, such that for a particular value of the gauge coupling the theory has a self-dual symmetry. The self-dual symmetry turns out to be a generator of a group which is a central extension of $\mathbb Z_4$ by the lattice translation symmetry group. The simplest case amenable to numerical simulations is the case when there is exactly one electrically and one magnetically charged boson. We discuss the phase structure of this theory and the nature of the self-dual symmetry in detail. Using a suitable worldline representation of the system we present the results of numerical simulations that support the conjectured phase diagram.