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371
Liouville Correlation Functions from Fourdimensional Gauge Theories
 SIMONS CENTER FOR GEOMETRY AND PHYSICS, STONY BROOK UNIVERSITY
, 2009
"... We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N = 2 SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture ..."
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Cited by 393 (22 self)
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We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N = 2 SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture at genus 0, 1.
AN−1 conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
, 2009
"... We propose a relation between correlation functions in the 2d AN−1 conformal Toda theories and the Nekrasov instanton partition functions in certain conformal N = 2 SU(N) 4d quiver gauge theories. Our proposal generalises the recently uncovered relation between the Liouville theory and SU(2) quivers ..."
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Cited by 158 (4 self)
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We propose a relation between correlation functions in the 2d AN−1 conformal Toda theories and the Nekrasov instanton partition functions in certain conformal N = 2 SU(N) 4d quiver gauge theories. Our proposal generalises the recently uncovered relation between the Liouville theory and SU(2) quivers [1]. New features appear in the analysis that have no counterparts in the Liouville case.
Lectures on localization and matrix models in Supersymmetric Chern–simons–matter Theories
, 2012
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Twisted supersymmetric 5D YangMills theory and contact geometry
 JHEP
, 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 ..."
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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.
ChernSimons Theory with Vector Fermion Matter,” [arXiv:1110.4386 [hepth
"... We study three dimensional conformal field theories described by U(N) ChernSimons theory at level k coupled to massless fermions in the fundamental representation. By solving a SchwingerDyson equation in lightcone gauge, we compute the exact planar free energy of the theory at finite temperature ..."
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Cited by 39 (2 self)
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We study three dimensional conformal field theories described by U(N) ChernSimons theory at level k coupled to massless fermions in the fundamental representation. By solving a SchwingerDyson equation in lightcone gauge, we compute the exact planar free energy of the theory at finite temperature on R2 as a function of the ’t Hooft coupling λ = N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at λ  = 1; the conformal theory does not exist for λ > 1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three point functions up to two loops. We also discuss a lightcone Hamiltonian formulation of this theory where a W ∞ algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory. ar X iv