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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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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.
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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Cited by 6 (0 self)
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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.
Instanton Effects in ABJM Theory from Fermi Gas Approach, JHEP 1301 (2013) 158, [arXiv:1211.1251
 Instanton Bound States in ABJM Theory, JHEP 1305 (2013) 054, [arXiv:1301.5184
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Partition Functions of Superconformal ChernSimons Theories from Fermi Gas Approach
, 2014
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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
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"... The partition function on the threesphere of N = 3 ChernSimonsmatter theories can be formulated in terms of an ideal Fermi gas. In this paper we show that, in theories with N = 2 supersymmetry, the partition function corresponds to a gas of interacting fermions in one dimension. The large N limit ..."
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The partition function on the threesphere of N = 3 ChernSimonsmatter theories can be formulated in terms of an ideal Fermi gas. In this paper we show that, in theories with N = 2 supersymmetry, the partition function corresponds to a gas of interacting fermions in one dimension. The large N limit is the thermodynamic limit of the gas and it can be analyzed with the Hartree and ThomasFermi approximations, which lead to the known large N solutions of these models. We use this interacting fermion picture to analyze in detail N = 2 theories with one single node. In the case of theories with no longrange forces we incorporate exchange effects and argue that the partition function is given by an Airy function, as in N = 3 theories. For the theory with g adjoint superfields and longrange forces, the ThomasFermi approximation leads to an integral equation which determines the large N, strongly coupled Rcharge
ABJM Wilson loops in the Fermi . . .
, 2013
"... The matrix model of ABJM theory can be formulated in terms of an ideal Fermi gas with a nontrivial oneparticle Hamiltonian. We show that, in this formalism, vevs of Wilson loops correspond to averages of operators in the statisticalmechanical problem. This makes it possible to calculate these v ..."
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The matrix model of ABJM theory can be formulated in terms of an ideal Fermi gas with a nontrivial oneparticle Hamiltonian. We show that, in this formalism, vevs of Wilson loops correspond to averages of operators in the statisticalmechanical problem. This makes it possible to calculate these vevs at all orders in 1/N, up to exponentially small corrections, and for arbitrary Chern–Simons coupling, by using the WKB expansion. We present explicit results for the vevs of 1/6 and the 1/2 BPS Wilson loops, at any winding number, in terms of Airy functions. Our expressions are shown to reproduce the low genus results obtained previously in the ’t Hooft expansion.