We study the N=2 four-dimensional superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute. Extrapolating from the SU(2) generalized quivers, which have a Lagrangian description, we conjecture explicit formulae for all A-type quivers of class S, which in general do not have one. We test our proposals against several expected dualities. The index can always be interpreted as a correlator in a two-dimensional topological theory, which we identify in each limit as a certain deformation of two-dimensional Yang-Mills theory. The structure constants of the topological algebra are diagonal in the basis of Macdonald polynomials of the holonomies.Comment: 57 pages, 6 figures; v2: references added and minor improvements; v3: typos correcte

We show that the superconformal index (the partition function on the three-sphere times a circle) of a certain class of 4D supersymmetric field theories is exactly equal to a partition function of q-deformed nonsupersymmetric 2D Yang-Mills theory.

We derive an integral representation for the superconformal index of the stronglycoupled N = 2 superconformal field theory with E 6 flavor symmetry. The explicit expression of the index allows highly non-trivial checks of Argyres-Seiberg duality and of a class of S-dualities conjectured by Gaiotto.

We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d N = (2, 0) theory of type J on a punctured sphere. We denote the AD theories as (and Y represent an irregular and a regular singularity respectively. We restrict to the 'minimal' case where J b [k] has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to the AD theory is conjectured to be the Walgebra W k 2d (J, Y ), where k 2d = −h + b b+k with h being the dual Coxeter number of J. We verify this conjecture by showing that the Schur index of the AD theory is identical to the vacuum character of the corresponding VOA, and the Hall-Littlewood index computes the Hilbert series of the Higgs branch. We also find that the Schur and Hall-Littlewood index for the AD theory can be written in a simple closed form for b = h. We also test the conjecture that the associated variety of such VOA is identical to the Higgs branch. The M5-brane construction of these theories and the corresponding TQFT structure of the index play a crucial role in our computations.

We show that the N =1 supersymmetric SU (N ) gauge theory with 2N flavors without superpotential has not only the standard Seiberg dual description but also another dual description involving two copies of the so-called T N theory. This is a natural generalization to N > 2 of a dual description of SU (2) gauge theory with 4 flavors found by Csaki, Schmaltz, Skiba and Terning. We also study dualities of other N =1 SCFTs involving copies of T N theories. Our duality is the basic operation from which a recently-found web of N =1 dualities obtained by compactifying M5-branes on Riemann surfaces can be derived field-theoretically.

Abstract:The superconformal index of a 4d gauge theory is computed by a matrix integral arising from localization of the supersymmetric path integral on S 3 × S 1 to the saddle point. As the radius of the circle goes to zero, it is natural to expect that the 4d path integral becomes the partition function of dimensionally reduced gauge theory on S 3 . We show that this is indeed the case and recover the matrix integral of Kapustin, Willett and Yaakov from the matrix integral that computes the superconformal index. Remarkably, the superconformal index of the "parent" 4d theory can be thought of as the q-deformation of the 3d partition function.

We study a class of two-dimensional N = (0, 4) quiver gauge theories that flow to superconformal field theories. We find dualities for the superconformal field theories similar to the 4d N = 2 theories of class S, labelled by a Riemann surface C. The dual descriptions arise from various pair-of-pants decompositions, that involve an analog of the T N theory. Especially, we find the superconformal indices of such theories can be written in terms of a topological field theory on C. We interpret this class of SCFTs as the ones coming from compactifying 6d N = (2, 0) theory on CP 1 ×C. Moreover, some new dualities of (0, 2) and (2, 2) theories are also discussed.

Abstract:We evaluate the superconformal index of the Y p,q quiver gauge theories using Römeslberger's prescription. For the conifold quiver Y 1,0 we find exact agreement at large N with a previous calculation in the dual AdS 5 × T