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arXiv · 1812.02832

Anomalies and Holomorphy in Supersymmetric Chern-Simons-Matter Theories

Nathaniel Bade·Chris Beasley
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Abstract

For Chern-Simons-matter theories in three dimensions, gauge invariance may require the Chern-Simons level k to be half-integral, in which case parity is violated. As noted by Pasquetti for abelian theories with N=2 supersymmetry, the partition function on the ellipsoid also admits a suitable holomorphic factorization precisely when the value of k is properly quantized. Using known formulas for the partition function, we investigate analytic aspects of this factorization for non-abelian gauge groups and general matter representations. We verify that factorization occurs in accord with the parity anomaly for the classical matrix groups and for the exceptional group G_2. In an appendix, we discuss the analytic continuation of torus knot observables in the SU(2) Chern-Simons-matter theory.

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Nathaniel Bade, Chris Beasley. 2018-12-06. Anomalies and Holomorphy in Supersymmetric Chern-Simons-Matter Theories. https://arxiv.org/abs/1812.02832

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