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The large N limit of toric . . .
, 2011
"... We compute the large N limit of the localized three dimensional free energy of various field theories with known proposed AdS duals. We show that vectorlike theories agree with the expected supergravity results, and with the conjectured Ftheorem. We also check that the large N free energy is pre ..."
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We compute the large N limit of the localized three dimensional free energy of various field theories with known proposed AdS duals. We show that vectorlike theories agree with the expected supergravity results, and with the conjectured Ftheorem. We also check that the large N free energy is preserved by the three dimensional Seiberg duality for general classes of vector like theories. Then we analyze the behavior of the free energy of chirallike theories by applying a new proposal. The proposal is based on the restoration of a discrete symmetry on the free energy before the extremization. We apply this procedure at strong coupling in some examples and we discuss the results. We conclude the paper by proposing an alternative geometrical expression for the free energy.
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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
Threesphere free energy for classical gauge groups
, 2013
"... Abstract: In this note, we calculate the S3 free energy F of 3d N ≥ 4 supersymmetric gauge theories with U(N), O(N), and USp(2N) gauge groups and matter hypermultiplets in the fundamental and twoindex tensor representations. Supersymmetric localization reduces the computation of F to a matrix mode ..."
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Abstract: In this note, we calculate the S3 free energy F of 3d N ≥ 4 supersymmetric gauge theories with U(N), O(N), and USp(2N) gauge groups and matter hypermultiplets in the fundamental and twoindex tensor representations. Supersymmetric localization reduces the computation of F to a matrix model that we solve in the large N limit using two different methods. The first method is a saddle point approximation first introduced in [1], which we extend to nexttoleading order in 1/N. The second method generalizes the Fermi gas approach of [2] to theories with symplectic and orthogonal gauge groups, and yields an expression for F valid to all orders in 1/N. In developing the second method, we use a nontrivial generalization of the Cauchy determinant formula.
Topics in supersymmetric quantum field theory
, 2013
"... This thesis describes several new tools for analyzing supersymmetric quantum field theories, focusing on theories with four supercharges in three and four dimensions. In chapter two, we discuss supercurrents, supersymmetry multiplets that include the energymomentum tensor. Physically, different sup ..."
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This thesis describes several new tools for analyzing supersymmetric quantum field theories, focusing on theories with four supercharges in three and four dimensions. In chapter two, we discuss supercurrents, supersymmetry multiplets that include the energymomentum tensor. Physically, different supercurrents give rise to different brane charges in the supersymmetry algebra. They also encode different ways of placing supersymmetric field theories on a curved manifold. Under certain conditions this procedure preserves some of the supersymmetry. In chapter three, we explore these conditions for the case of fourdimensional N = 1 theories with a U(1)R symmetry. In particular, we find that a manifold admits a single supercharge if and only if it is Hermitian. In chapter four, we shift the focus to threedimensional field theories. We study ChernSimons contact terms – contact terms of conserved currents and the energymomentum tensor, which are associated with ChernSimons terms for background fields. While the integer parts of these contact terms are ambiguous, their fractional parts constitute new meaningful observables. In N = 2 supersymmetric theories with a U(1)R symmetry certain
Z Extremization in ChiralLike Chern Simons
"... Abstract: We study the localized free energy on S3 of threedimensional N = 2 ChernSimons matter theories at weak coupling. We compute the two loop R charge in three different ways, namely by the standard perturbative approach, by extremizing the localized partition function at finite N and by app ..."
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Abstract: We study the localized free energy on S3 of threedimensional N = 2 ChernSimons matter theories at weak coupling. We compute the two loop R charge in three different ways, namely by the standard perturbative approach, by extremizing the localized partition function at finite N and by applying the standard saddle point approximation for large N. We show that the latter approach does not reproduce the expected result when chiral theories are considered. We circumvent these problems by restoring a reflection symmetry on the eigenvalues in the free energy. Thanks to this symmetrization we find that the three methods employed agree. In particular we match the computation for a model whose four dimensional parent is the quiver gauge theory describing D3 branes probing the Hirzebruch surface. We conclude by commenting on the application of our results and to the strong coupling regime.ar X iv
Prepared for submission to JHEP Holography of 3d3d correspondence at Large N
"... Abstract: We study the physics of multiple M5branes compactified on a hyperbolic 3manifold. On the one hand, it leads to the 3d3d correspondence which maps an N = 2 superconformal field theory to a pure ChernSimons theory on the 3manifold. On the other hand, it leads to a warped AdS4 geometry i ..."
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Abstract: We study the physics of multiple M5branes compactified on a hyperbolic 3manifold. On the one hand, it leads to the 3d3d correspondence which maps an N = 2 superconformal field theory to a pure ChernSimons theory on the 3manifold. On the other hand, it leads to a warped AdS4 geometry in Mtheory holographically dual to the superconformal field theory. Combining the holographic duality and the 3d3d correspondence, we propose a conjecture for the large N limit of the perturbative free energy of a ChernSimons theory on hyperbolic 3manifold. The conjecture claims that the tree, oneloop and twoloop terms all share the same N3 scaling behavior and are proportional to the volume of the 3manifold, while the threeloop and higher terms are suppressed at large N. Under mild assumptions, we prove the tree and oneloop parts of the conjecture. For the twoloop part, we test the conjecture numerically in a number of examples and find precise agreement. We also confirm the suppression of higher loop terms in a few examples. ar X iv