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

Clay Cordova, Po-Shen Hsin, Nathan Seiberg

SciPost Phys. 4, 021 (2018) · published 29 April 2018


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.

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Chern-Simons theory Counterterms Dualities Gauge theory Global symmetries Level-rank duality Orthogonal groups Topological quantum field theories (TQFT)

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