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The exact superconformal R-symmetry extremizes Z

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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.

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  1. Institute for Advanced Study, Einstein Drive, Princeton, NJ, 08540, U.S.A

    Daniel L. Jafferis

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Correspondence to Daniel L. Jafferis.

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ArXiv ePrint: 1012.3210

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Jafferis, D.L. The exact superconformal R-symmetry extremizes Z. J. High Energ. Phys. 2012, 159 (2012). https://doi.org/10.1007/JHEP05(2012)159

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