The exact superconformal R-symmetry extremizes Z

By D. Jafferis. 2010

782 citations recorded by the source corpus.

A bstractThe 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.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ae4473ae93794ca30281350b3e659da49e8dcb8e

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Citations in the corpus

Black hole microstates in AdS4 from supersymmetric localization (2015, background): “In odd dimensions, we have so far the example of three dimensions where the partition function on S3 is extremized [21, 24, 25].”
4d Index to 3d Index and 2d TQFT (2011, background): “Recent studies have uncovered powerful techniques (mostly based on localization) to extract exact results for 3d and 4d supersymmetric gauge theories, including the 4d N ≥ 1 superconformal index on S(1) × S(3) [1, 2], the 4d N ≥ 2 partition function on S(4) [3], the 3d N ≥ 2 partition function on S(”
Exploring curved superspace (2012, background): “Following [7-10], much work has focused on supersymmetric theories on round spheres.”
Comments on Chern-Simons contact terms in three dimensions (2012, methodology): “Alternatively, we can determine t by applying the F -maximization principle, which was conjectured in [27,28] and proved”
On the CFT operator spectrum at large global charge (2015, background): “(4)This theory can be shown to flow to a nontrivial fixed point by various means, such as the computation of the two-point function of the R-current in the infrared [15, 16].”
A universal counting of black hole microstates in AdS4 (2017, methodology): “Under this condition, the logarithm of the topologically twisted index is given by5 logZ(∆I , nI) = (1− g)i ( 2 π V(∆I) + ∑ I [( nI 1− g − ∆I π ) ∂V ∂∆I ]) , (2.5) where the function V was called Bethe potential in [4] and is the Yang-Yang function of an associated integrable system [33, 9].6 Quite ”
Top down approach to 6D SCFTs (2018, background): “In D = 3, there is a related F-theorem [155–157].”
Seiberg-Witten theories on ellipsoids (2012, result): “Similar exact results have also been obtained for 3D N ≥ 2 gauge theories on round three-sphere [3, 4, 5], its orbifold [6, 7], and 2D theories on sphere [8, 9].”
The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere (2012, background): “2) defines the function l(y) which appeared previously in Jafferis’s work [10] on localization in 3D theories with matter.”
Exact Kähler potential from gauge theory and mirror symmetry (2012, background): “In [16] the authors have pointed out that superconformality and unitarity are not respected in the framework of the exact three-sphere partition function [17, 18, 19] due to unitarity violating terms inevitable when putting rigid supersymmetric theories on a curved manifold, even though the theories”
Notes on SUSY gauge theories on three-sphere (2010, background): “Jafferis [22] which has significant overlap with ours.”
Localization techniques in quantum field theories (2016, methodology): “The whole volume, when published, could be cited as V. Pestun and M. Zabzine, eds., “Localization techniques in quantum field theories”, Journal of Physics A (2016) The arXiv preprint version can be accessed from arXiv summary entry which lists all authors and links to all 17 individual contribution”
N=2 supersymmetric theories on squashed three-sphere (2011, methodology): “The partition function for general Weyl weight assignments is computed in [5, 6].”
Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories (2011, methodology): “55) can be easily computed by using ζ-function regularization [55, 48].”