Interacting fermions and N=2 Chern-Simons-matter theories

The partition function on the three-sphere of N=3 Chern-Simons-matter 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 Thomas-Fermi 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 long-range 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 long-range forces, the Thomas-Fermi approximation leads to an integral equation which determines the large N, strongly coupled R-charge.Comment: 29 pages, 4 figure

Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification

We consider N=3 supersymmetric Chern-Simons (CS) theories that contain product U(N) gauge groups and bifundamental matter fields. Using the matrix model of Kapustin, Willett and Yaakov, we examine the Euclidean partition function of these theories on an S^3 in the large N limit. We show that the only such CS theories for which the long range forces between the eigenvalues cancel have quivers which are in one-to-one correspondence with the simply laced affine Dynkin diagrams. As the A_n series was studied in detail before, in this paper we compute the partition function for the D_4 quiver. The D_4 example gives further evidence for a conjecture that the saddle point eigenvalue distribution is determined by the distribution of gauge invariant chiral operators. We also see that the partition function is invariant under a generalized Seiberg duality for CS theories.Comment: 20 pages, 3 figures; v2 refs added; v3 conventions in figure 3 altered, version to appear in JHE

Large N Free Energy of 3d N=4 SCFTs and AdS/CFT

We provide a non-trivial check of the AdS_4/CFT_3 correspondence recently proposed in arXiv:1106.4253 by verifying the GKPW relation in the large N limit. The CFT free energy is obtained from the previous works (arXiv:1105.2551, arXiv:1105.4390) on the S^3 partition function for 3-dimensional N=4 SCFT T[SU(N)]. This is matched with the computation of the type IIB action on the corresponding gravity background. We unexpectedly find that the leading behavior of the free energy at large N is 1/2 N^2 ln N. We also extend our results to richer theories and argue that 1/2 N^2 ln N is the maximal free energy at large N in this class of gauge theories.Comment: 20 pages, 3 figure

Operator Counting and Eigenvalue Distributions for 3D Supersymmetric Gauge Theories

We give further support for our conjecture relating eigenvalue distributions of the Kapustin-Willett-Yaakov matrix model in the large N limit to numbers of operators in the chiral ring of the corresponding supersymmetric three-dimensional gauge theory. We show that the relation holds for non-critical R-charges and for examples with {\mathcal N}=2 instead of {\mathcal N}=3 supersymmetry where the bifundamental matter fields are nonchiral. We prove that, for non-critical R-charges, the conjecture is equivalent to a relation between the free energy of the gauge theory on a three sphere and the volume of a Sasaki manifold that is part of the moduli space of the gauge theory. We also investigate the consequences of our conjecture for chiral theories where the matrix model is not well understood.Comment: 27 pages + appendices, 5 figure

The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals

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 vector-like theories agree with the expected supergravity results, and with the conjectured F-theorem. 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 chiral-like 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.Comment: 40 pages, 7 figures, using jheppub.sty, references adde

Relation between the 4d superconformal index and the S^3 partition function

A relation between the 4d superconformal index and the S^3 partition function is studied with focus on the 4d and 3d actions used in localization. In the case of vanishing Chern-Simons levels and round S^3 we explicitly show that the 3d action is obtained from the 4d action by dimensional reduction up to terms which do not affect the exact results. By combining this fact and a recent proposal concerning a squashing of S^3 and SU(2) Wilson line, we obtain a formula which gives the partition function depending on the Weyl weight of chiral multiplets, real mass parameters, FI parameters, and a squashing parameter as a limit of the index of a parent 4d theory.Comment: 20 pages, LaTeX; v2: comments added; v3: minor corrections, version published in JHE

The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories

We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix model. The saddlepoint equations in a large N limit lead to a constraint that the long range forces between the eigenvalues must cancel; the resulting quiver theories are of affine Dynkin type. We introduce a folding/unfolding trick which lets us, at the level of the large N matrix model, (i) map quivers with orthosymplectic groups to those with unitary groups, and (ii) obtain non-simply laced quivers from the corresponding simply laced quivers using a Z_2 outer automorphism. The brane configurations of the quivers are described in string theory and the folding/unfolding is interpreted as the addition/subtraction of orientifold and orbifold planes. We also relate the U(N) quiver theories to the affine ADE quiver matrix models with a Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in 2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.Comment: 30 pages, 5 figure

Massive type IIA string theory cannot be strongly coupled

Understanding the strong coupling limit of massive type IIA string theory is a longstanding problem. We argue that perhaps this problem does not exist; namely, there may be no strongly coupled solutions of the massive theory. We show explicitly that massive type IIA string theory can never be strongly coupled in a weakly curved region of space-time. We illustrate our general claim with two classes of massive solutions in AdS4xCP3: one, previously known, with N = 1 supersymmetry, and a new one with N = 2 supersymmetry. Both solutions are dual to d = 3 Chern-Simons-matter theories. In both these massive examples, as the rank N of the gauge group is increased, the dilaton initially increases in the same way as in the corresponding massless case; before it can reach the M-theory regime, however, it enters a second regime, in which the dilaton decreases even as N increases. In the N = 2 case, we find supersymmetry-preserving gauge-invariant monopole operators whose mass is independent of N. This predicts the existence of branes which stay light even when the dilaton decreases. We show that, on the gravity side, these states originate from D2-D0 bound states wrapping the vanishing two-cycle of a conifold singularity that develops at large N.Comment: 43 pages, 5 figures. v2: added reference

New Gauged Linear Sigma Models for 8D HyperKahler Manifolds and Calabi-Yau Crystals

We propose two kinds of gauged linear sigma models whose moduli spaces are real eight-dimensional hyperKahler and Calabi-Yau manifolds, respectively. Here, hyperKahler manifolds have sp(2) holonomy in general and are dual to Type IIB (p,q)5-brane configurations. On the other hand, Calabi-Yau fourfolds are toric varieties expressed as quotient spaces. Our model involving fourfolds is different from the usual one which is directly related to a symplectic quotient procedure. Remarkable features in newly-found three-dimensional Chern-Simons-matter theories appear here as well, such as dynamical Fayet-Iliopoulos parameters, one dualized photon and its residual discrete gauge symmetry.Comment: 20 pages, 1 figure; v2: minor changes and references added; v3: statements improved, newer than JHEP versio

Refined Checks and Exact Dualities in Three Dimensions

We discuss and provide nontrivial evidence for a large class of dualities in three-dimensional field theories with different gauge groups. We match the full partition functions of the dual phases for any value of the couplings to underpin our proposals. We focus on two classes of models. The first class, motivated by the AdS/CFT conjecture, consists of necklace U(N) quiver gauge theories with non chiral matter fields. We also consider orientifold projections and establish dualities among necklace quivers with alternating orthogonal and symplectic groups. The second class consists of theories with tensor matter fields with free theory duals. In most of these cases the R-symmetry mixes with IR accidental symmetries and we develop the prescription to include their contribution into the partition function and the extremization problem accordingly.Comment: 38 pages, 3 figure, using jheppu