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Liouville Correlation Functions from Four-dimensional 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 Yang-Mills theory and contact geometry
- JHEP
, 2012
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Multi-Matrix Models and Tri-Sasaki Einstein Spaces
, 2010
"... Localization methods reduce the path integrals in N ≥ 2 supersymmetric Chern-Simons gauge theories on S 3 to multi-matrix integrals. A recent evaluation of such a two-matrix 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 Chern-Simons gauge theories on S 3 to multi-matrix integrals. A recent evaluation of such a two-matrix 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 p-matrix integrals describing N = 3 superconformal U(N) p Chern-Simons 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 Chern-Simons levels ki fixed. The dual M-theory backgrounds are AdS4×Y, where Y are seven-dimensional tri-Sasaki 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 p-matrix free energies that agrees with the available results for volumes of the tri-Sasaki Einstein spaces Y, thus providing a thorough test of the corresponding AdS4/CFT3 dualities. This formula is consistent with the Seiberg duality conjectured for Chern-Simons gauge theories.
Chern-Simons Theory with Vector Fermion Matter,” [arXiv:1110.4386 [hepth
"... We study three dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental repre-sentation. By solving a Schwinger-Dyson equation in lightcone gauge, we com-pute 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) Chern-Simons theory at level k coupled to massless fermions in the fundamental repre-sentation. By solving a Schwinger-Dyson equation in lightcone gauge, we com-pute 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 con-formal 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 lead-ing 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
