The Exact Superconformal R-Symmetry Extremizes Z

Details The Exact Superconformal R-Symmetry Extremizes Z The Exact Superconformal R-Symmetry Extremizes Z

2010-12-15

arxiv.org/abs/1012.3210v2

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

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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