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23
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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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 N = 8 Superconformal Bootstrap in Three Dimensions
, 2014
"... We analyze the constraints imposed by unitarity and crossing symmetry on the fourpoint function of the stresstensor multiplet of N = 8 superconformal field theories in three dimensions. We first derive the superconformal blocks by analyzing the superconformal Ward identity. Our results imply that ..."
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We analyze the constraints imposed by unitarity and crossing symmetry on the fourpoint function of the stresstensor multiplet of N = 8 superconformal field theories in three dimensions. We first derive the superconformal blocks by analyzing the superconformal Ward identity. Our results imply that the OPE of the primary operator of the stresstensor multiplet with itself must have parity symmetry. We then analyze the relations between the crossing equations, and we find that these equations are mostly redundant. We implement the independent crossing constraints numerically and find bounds on OPE coefficients and operator dimensions as a function of the stresstensor central charge. To make contact with known N = 8 superconformal field theories, we compute this central charge in a few particular cases using supersymmetric localization. For limiting values of the central charge, our numerical bounds are nearly saturated by the large N limit of ABJM theory and also by the free U(1) × U(1) ABJM theory.
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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
ABJ Wilson loops and Seiberg Duality
, 2014
"... We study supersymmetric Wilson loops in the N = 6 supersymmetric U(N1)k × U(N2)−k ChernSimonsmatter (CSM) theory, the ABJ theory, at finite N1, N2 and k. This generalizes our previous study on the ABJ partition function. First computing the Wilson loops in the U(N1) × U(N2) lens space matrix mode ..."
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We study supersymmetric Wilson loops in the N = 6 supersymmetric U(N1)k × U(N2)−k ChernSimonsmatter (CSM) theory, the ABJ theory, at finite N1, N2 and k. This generalizes our previous study on the ABJ partition function. First computing the Wilson loops in the U(N1) × U(N2) lens space matrix model exactly, we perform an analytic continuation, N2 to −N2, to obtain the Wilson loops in the ABJ theory that is given in terms of a formal series and only valid in perturbation theory. Via a SommerfeldWatson type transform, we provide a nonperturbative completion that renders the formal series welldefined at all couplings. This is given by min(N1, N2)dimensional integrals that generalize the “mirror description ” of the partition function of the ABJM theory. Using our results, we find the maps between the Wilson loops in the original and Seiberg dual theories and prove the duality. In our approach we can explicitly see how the perturbative and nonperturbative contributions to the Wilson loops are exchanged under the duality. The duality maps are further supported by a heuristic yet very useful argument based on the brane configuration as well as an alternative derivation based on that of Kapustin and Willett.