The Exact Superconformal R-Symmetry Extremizes Z

Abstract

The three sphere partition function, Z, of three dimensional theories with four supercharges and an R-symmetry is computed using localization, resulting in a matrix integral over the Cartan of the gauge group. There is a family of couplings to the curved background, parameterized by a choice of R-charge, such that supersymmetry is preserved; Z is a function of those parameters. The magnitude of the result is shown to be extremized for the superconformal R-charge of the infrared conformal field theory, in the absence of mixing of the R-symmetry with accidental symmetries. This exactly determines the IR superconformal R-charge.

25 pages, v2: references added, typos and an error in a formula corrected

References in corpus (7)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Towards a derivation of holographic entanglement entropy
• Holographic c-theorems in arbitrary dimensions
• Notes on SUSY Gauge Theories on Three-Sphere
• AGT on the S-duality Wall
• Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories
• Comments on scaling limits of 4d N=2 theories

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