Quantum Phases of $4d$ $SU(N)$ $\mathcal{N}=4$ SYM

TL;DR

This paper proposes that 4d $SU(N)$ $ abla=4$ SYM exhibits a line of zero-temperature topologically ordered phases characterized by bound states charged under one-form symmetries, related to conformal blocks of an $SU(N)_1$ WZNW model.

Contribution

It introduces a novel perspective on the phase structure of 4d $SU(N)$ $ abla=4$ SYM, linking topological order to conformal field theory constructs.

Findings

Identification of an accumulation line of topologically ordered phases.

Description of bound states with two dyonic flux components.

Connection to $SU(N)_1$ WZNW model on a two-torus.

Abstract

It is argued that $4d$ $SU(N)$ $\mathcal{N}=4$ SYM has an accumulation line of zero-temperature topologically ordered phases. Each of these phases corresponds to $N$ bound states charged under electromagnetic $\mathbb{Z}^{(1)}_N$ one-form symmetries. Each of the $N$ bound states is made of two Dyonic flux components each of them extended over a two dimensional surface. They are localized at the fixed loci of a rotational action, and are argued to correspond to conformal blocks (or primaries) of an $SU(N)_1$ WZNW model on a two-torus.