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22
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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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.
Article Reference Mtheoretic matrix models
"... Some matrix models admit, on top of the usual ’t Hooft expansion, an Mtheorylike expansion, i.e. an expansion at large N but where the rest of the parameters are fixed, instead of scaling with N. These models, which we call Mtheoretic matrix models, appear in the localization of ChernSimonsmatt ..."
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Some matrix models admit, on top of the usual ’t Hooft expansion, an Mtheorylike expansion, i.e. an expansion at large N but where the rest of the parameters are fixed, instead of scaling with N. These models, which we call Mtheoretic matrix models, appear in the localization of ChernSimonsmatter theories, and also in twodimensional statistical physics. Generically, their partition function receives nonperturbative corrections which are not captured by the ’t Hooft expansion. In this paper, we discuss general aspects of these type of matrix integrals and we analyze in detail two different examples. The first one is the matrix model computing the partition function of N = 4 $ $ \mathcal{N}=4 $ $ supersymmetric YangMills theory in three dimensions with one adjoint hypermultiplet and N f fundamentals, which has a conjectured Mtheory dual, and which we call the N f matrix model. The second one, which we call the polymer matrix model, computes form factors of the 2d Ising model and is related to the physics of 2d polymers. In both cases we determine their exact planar limit. In the N f matrix model, the planar free [...]
Article Reference Exact results in N = 8 $ $ \mathcal{N}=8 $ $ ChernSimonsmatter theories and quantum geometry
"... We show that, in ABJ(M) theories with N = 8 $ $ \mathcal{N}=8 $ $ supersymmetry, the nonperturbative sector of the partition function on the threesphere simplifies drastically. Due to this simplification, we are able to write closed form expressions for the grand potential of these theories, which ..."
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We show that, in ABJ(M) theories with N = 8 $ $ \mathcal{N}=8 $ $ supersymmetry, the nonperturbative sector of the partition function on the threesphere simplifies drastically. Due to this simplification, we are able to write closed form expressions for the grand potential of these theories, which determines the full large N asymptotics. Moreover, we find explicit formulae for the generating functionals of their partition functions, for all values of the rank N of the gauge group: they involve Jacobi theta functions on the spectral curve associated to the planar limit. Exact quantization conditions for the spectral problem of the Fermi gas are then obtained from the vanishing of the theta function. We also show that the partition function, as a function of N, can be extended in a natural way to an entire function on the full complex plane, and we explore some possible consequences of this fact for the quantum geometry of Mtheory and for putative de Sitter extensions.
Quantization conditions and . . .
"... The partition function of ABJ(M) theories on the threesphere can be regarded as the canonical partition function of an ideal Fermi gas with a nontrivial Hamiltonian. We propose an exact expression for the spectral determinant of this Hamiltonian, which generalizes recent results obtained in the ma ..."
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The partition function of ABJ(M) theories on the threesphere can be regarded as the canonical partition function of an ideal Fermi gas with a nontrivial Hamiltonian. We propose an exact expression for the spectral determinant of this Hamiltonian, which generalizes recent results obtained in the maximally supersymmetric case. As a consequence, we find an exact WKB quantization condition determining the spectrum which is in agreement with numerical results. In addition, we investigate the factorization properties and functional equations for our conjectured spectral determinants. These functional equations relate the spectral determinants of ABJ theories with consecutive ranks of gauge groups but the same ChernSimons coupling.