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33
Lectures on localization and matrix models in Supersymmetric Chern–simons–matter Theories
, 2012
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MultiMatrix Models and TriSasaki Einstein Spaces
, 2010
"... Localization methods reduce the path integrals in N ≥ 2 supersymmetric ChernSimons gauge theories on S 3 to multimatrix integrals. A recent evaluation of such a twomatrix integral for the N = 6 superconformal U(N) × U(N) ABJM theory produced detailed agreement with the AdS/CFT correspondence, ex ..."
Abstract

Cited by 46 (2 self)
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Localization methods reduce the path integrals in N ≥ 2 supersymmetric ChernSimons gauge theories on S 3 to multimatrix integrals. A recent evaluation of such a twomatrix integral for the N = 6 superconformal U(N) × U(N) ABJM theory produced detailed agreement with the AdS/CFT correspondence, explaining in particular the N 3/2 scaling of the free energy. We study a class of pmatrix integrals describing N = 3 superconformal U(N) p ChernSimons gauge theories. We present a simple method that allows us to evaluate the eigenvalue densities and the free energies in the large N limit keeping the ChernSimons levels ki fixed. The dual Mtheory backgrounds are AdS4×Y, where Y are sevendimensional triSasaki Einstein spaces specified by the ki. The gravitational free energy scales inversely with the square root of the volume of Y. We find a general formula for the pmatrix free energies that agrees with the available results for volumes of the triSasaki Einstein spaces Y, thus providing a thorough test of the corresponding AdS4/CFT3 dualities. This formula is consistent with the Seiberg duality conjectured for ChernSimons gauge theories.
FTheorem without Supersymmetry
, 2011
"... The conjectured Ftheorem for threedimensional field theories states that the finite part of the free energy on S3 decreases along RG trajectories and is stationary at the fixed points. In previous work various successful tests of this proposal were carried out for theories with N = 2 supersymmetry ..."
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Cited by 17 (2 self)
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The conjectured Ftheorem for threedimensional field theories states that the finite part of the free energy on S3 decreases along RG trajectories and is stationary at the fixed points. In previous work various successful tests of this proposal were carried out for theories with N = 2 supersymmetry. In this paper we perform more general tests that do not rely on supersymmetry. We study perturbatively the RG flows produced by weakly relevant operators and show that the free energy decreases monotonically. We also consider large N field theories perturbed by relevant double trace operators, free massive field theories, and some ChernSimons gauge theories. In all cases the free energy in the IR is smaller than in the UV, consistent with the Ftheorem. We discuss other odddimensional Euclidean theories on Sd and provide evidence that (−1)(d−1)/2 log Z  decreases along RG flow; in the particular case d = 1 this is the wellknown gtheorem.
Eigenvalue Distributions in Matrix Models for ChernSimonsmatter Theories
 Nucl. Phys. B
, 2012
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Partition Functions of Superconformal ChernSimons Theories from Fermi Gas Approach
, 2014
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A Note on the Partition Function of ABJM theory on S3, Prog.Theor.Phys. 127 (2012) 229–242
 Exact Results on the ABJM Fermi Gas, JHEP 1210 (2012) 020, [arXiv:1207.4283], P. Putrov and M. Yamazaki, Exact ABJM Partition Function from TBA, Mod.Phys.Lett. A27 (2012) 1250200, [arXiv:1207.5066
, 2013
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