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Superconformal indices of threedimensional theories related by mirror symmetry,” arXiv:1103.4075 [hepth
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Unquenched flavor and tropical geometry in strongly coupled Chern–Simons–matter theories
, 2011
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Exact results for fivedimensional superconformal field theories with gravity duals,” arXiv:1207.4359 [hepth
"... We apply the technique of supersymmetric localization to exactly compute the S5 partition function of several large N superconformal field theories in five dimensions that have AdS6 duals in massive type IIA supergravity. The localization computations are performed in the nonrenormalizable effecti ..."
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We apply the technique of supersymmetric localization to exactly compute the S5 partition function of several large N superconformal field theories in five dimensions that have AdS6 duals in massive type IIA supergravity. The localization computations are performed in the nonrenormalizable effective field theories obtained through relevant deformations of the UV superconformal field theories. We compare the S5 free energy to a holographic computation of entanglement entropy in the AdS6 duals and find perfect agreement. In particular, we reproduce the N5/2 scaling of the S5 free energy that was expected from supergravity.
Nonperturbative effects and the refined topological string
, 2013
"... The partition function of ABJM theory on the threesphere has nonperturbative corrections due to membrane instantons in the Mtheory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi–Yau manifold known as lo ..."
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Cited by 23 (7 self)
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The partition function of ABJM theory on the threesphere has nonperturbative corrections due to membrane instantons in the Mtheory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi–Yau manifold known as local P1 × P1, in the Nekrasov–Shatashvili limit. Our result can be interpreted as a firstprinciples derivation of the full series of nonperturbative effects for the closed topological string on this Calabi–Yau background. Based on this, we make a proposal for the nonperturbative free energy of topological strings on general, local Calabi–Yau manifolds.
Eigenvalue Distributions in Matrix Models for ChernSimonsmatter Theories
 Nucl. Phys. B
, 2012
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The partition function of ABJ theory
, 2013
"... We study the partition function of the N = 6 supersymmetric U(N1)k × U(N2)−k ChernSimonsmatter (CSM) theory, also known as the ABJ theory. For this purpose, we first compute the partition function of the U(N1)×U(N2) lens space matrix model exactly. The result can be expressed as a product of qdef ..."
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We study the partition function of the N = 6 supersymmetric U(N1)k × U(N2)−k ChernSimonsmatter (CSM) theory, also known as the ABJ theory. For this purpose, we first compute the partition function of the U(N1)×U(N2) lens space matrix model exactly. The result can be expressed as a product of qdeformed Barnes Gfunction and a generalization of multiple qhypergeometric function. The ABJ partition function is then obtained from the lens space partition function by analytically continuing N2 to −N2. The answer is given by min(N1, N2)dimensional integrals and generalizes the “mirror description ” of the partition function of the ABJM theory, i.e. the N = 6 supersymmetric U(N)k × U(N)−k CSM theory. Our expression correctly reproduces perturbative expansions and vanishes for N1 − N2 > k in line with the conjectured supersymmetry breaking, and the Seiberg duality is explicitly checked for a class of nontrivial examples.