Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups

TL;DR

This paper explores dualities, counterterms, and anomalies in three-dimensional orthogonal gauge theories, revealing new boson-fermion dualities and extending phase diagram analyses for theories with various global gauge group forms.

Contribution

It derives level-rank duality for orthogonal gauge theories with discrete theta-parameters, including counterterms and anomaly analysis, and introduces new dualities involving matter fields.

Findings

Derived level-rank duality for $SO(N)_K$ theories with background fields.

Identified how counterterms shift when integrating out massive fermions.

Extended phase diagrams for theories with two-index tensor fermions.

Abstract

We study three-dimensional gauge theories based on orthogonal groups. Depending on the global form of the group these theories admit discrete $\theta$-parameters, which control the weights in the sum over topologically distinct gauge bundles. We derive level-rank duality for these topological field theories. Our results may also be viewed as level-rank duality for $SO(N)_{K}$ Chern-Simons theory in the presence of background fields for discrete global symmetries. In particular, we include the required counterterms and analysis of the anomalies. We couple our theories to charged matter and determine how these counterterms are shifted by integrating out massive fermions. By gauging discrete global symmetries we derive new boson-fermion dualities for vector matter, and present the phase diagram of theories with two-index tensor fermions, thus extending previous results for $SO(N)$ to other global forms of the gauge group.