Analytic framework for self-dual criticality in $\mathbb{Z}_k$ gauge theory with matter

TL;DR

This paper develops an analytic framework for understanding the multicritical point in 2+1D $ ext{Z}_k$ gauge theory with matter, revealing the role of duality symmetry and mutual Chern-Simons interactions in critical behavior.

Contribution

It introduces an effective U(1)×U(1) gauge theory with a mutual Chern-Simons term to describe the multicritical point and analyzes the scaling dimensions of operators in this context.

Findings

Monopoles are irrelevant in the IR conformal field theory.

Scaling dimensions approach 3 - 1/ν_{XY}^2 as k increases.

Analytic evidence for the role of duality symmetry in criticality.

Abstract

We study the putative multicritical point in 2+1D $\mathbb{Z}_k$ gauge theory where the Higgs and confinement transitions meet. The presence of an $e$-$m$ duality symmetry at this critical point forces anyons with nontrivial braiding to close their gaps simultaneously, giving rise to a critical theory that mixes strong interactions with mutual statistics. An effective U(1) $\times$ U(1) gauge theory with a mutual Chern-Simons term at level $k$ is proposed to describe the vicinity of the multicritical point for $k \geq 4$. We argue analytically that monopoles are irrelevant in the IR CFT and compute the scaling dimensions of the leading duality-symmetric/anti-symmetric operators. In the large $k$ limit, these scaling dimensions approach $3 - \nu_{\rm XY}^{-1}$ as $1/k^2$, where $\nu_{\rm XY}$ is the correlation length exponent of the 3D XY model.