FROM 4d SUPERCONFORMAL INDICES TO 3d PARTITION FUNCTIONS

By F. Dolan, V. Spiridonov, G. Vartanov. 2011

191 citations recorded by the source corpus.

Abstract An exact formula for partition functions in 3d field theories was recently suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific q-hypergeometric integrals whose key building block is the double sine function (or the hyperbolic gamma function). Elliptic hypergeometric integrals, discovered by the second author, define 4d superconformal indices. Using their reduction to the hyperbolic level, we describe a general scheme of reducing 4d superconformal indices to 3d partition functions which imply an efficient way of getting 3d N = 2 supersymmetric dualities for both SYM and CS theories from the “parent” 4d N = 1 dualities for SYM theories. As an example, we consider explicitly the duality pattern for 3d N = 2 SYM and CS theories with SP ( 2 N ) gauge group with the antisymmetric tensor matter.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c18461987e24b9c9be035af172f4f4ff6a219d67

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Citations in the corpus

Supersymmetry on curved spaces and holography (2012, methodology): “The partition function has already been used to check this extension of CS N = 2 Seiberg duality in three dimensions in [29, 141, 144, 173–176].”
Relation between the 4d superconformal index and the S3 partition function (2011, background): “The purpose of this paper is to extend the relation obtained in [23, 24] to general 3d N = 2 and 4d N = 1 theories, and to establish the relation at more fundamental level by comparing 3d and 4d actions.”
Gauge Theories and Macdonald Polynomials (2011, background): “opriate boundary conditions at the sexternal punctures and at the internal junctures. In a suitable limit, which corresponds to taking S1 (1) to be small, the 4dindex becomes the 3dpartition function [52, 53, 54], and our proposal reduces to the one of [75] (see also [76]). These authors show how to”
Bootstrapping the superconformal index with surface defects (2012, background): “ 3dtheory on a squashed S3. The reduction of the 4dindex to 3dpartition function is achieved by the following scaling of the fugacities, q= ei! 1; p= ei! 2; t= ei; a ‘= eim ‘; (7.1) and taking !0 [64, 65, 66], where a ‘ are 4d avor fugacities and m ‘ 3dreal masses. The 4dindex goes to the \ellipsoid”
N=2 supersymmetric theories on squashed three-sphere (2011, methodology): “It is used to check dualities among 3d field theories[7, 8, 9, 10, 11, 12, 13] and gauge/gravity”
Rigid supersymmetric theories in curved superspace (2011, methodology): “This fact has allowed [23,24,26-34] to compute Z”
Reducing the 4d index to the S3 partition function (2011, background): “ matrix model for N = 4 gauge theories with two supersymmetric deformations. One such deformation involving squashed S3 was studied in [17]. Note added: While this note was in preparation we received [18] in which the authors ﬁnd a mathematical relation between the 4d index and the S3 partition func”
Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories (2012, background): “8 Recently, it was found that various squashed spheres also admit rigid supersymmetry [44-50].”
3d dualities from 4d dualities (2013, background): “And indeed, looking at the Euclidean partition functions on S3 of the 3dtheories A and B, one ﬁnds that they are the same on this codimension-one subspace of their parameter space, but not in general [20,3]. In the eﬀective 3dtheory that we get at ﬁnite ras described above, the extra superpotential ”
The gravity dual of supersymmetric gauge theories on a squashed three-sphere (2011, background): “The matching of partition functions also allows one to perform non-trivial tests of conjectured dualities between pairs of three-dimensional field theories [18, 19, 20, 21, 22, 23, 24, 25, 26].”
Seiberg-Witten theories on ellipsoids (2012, background): “For other recent work on supersymmetric deformations of the round S3 with additional background fields, see [23, 24, 25, 26, 27, 28].”
Exploring curved superspace (2012, background): “) Recently, it was shown that rigid supersymmetry also exists on certain squashed spheres [13-19].”
Localization on Hopf surfaces (2014, background): “For this to be possible we need to show that the Gaussian action for fluctuations around the localization locus, resulting from the deformation terms δV , matches (23)Previous studies of relations between the index of four-dimensional gauge theories and the partition function in three dimensions inc”
5-dim superconformal index with enhanced En global symmetry (2012, background): “of scalar vev of the vector multiplet, from our index, which is analogous to the cases of 4d to 3d reduction considered in [51, 54, 52, 53] where 3d Chern-Simons terms cannot be obtained under the reduction.”
4d Index to 3d Index and 2d TQFT (2011, background): “(9)The same problem for p = 1 was analyzed in [12, 13, 14].”
Localization techniques in quantum field theories (2016, methodology): “by the superpotential, the superconformal R-symmetries can be determined through the c-extremization principle of [78,79].”
Supersymmetric field theories on three-manifolds (2012, background): “Following [1-4], much work has focused on supersymmetric theories on round and squashed spheres [5-13].”
Comments on 3d Seiberg-like dualities (2011, background): “The second kind of duality, more akin to Seiberg duality [5, 7, 8, 9, 10], has recently attracted renewed attention [11, 12, 13, 14, 15, 16, 17, 18, 19].”
The geometry of supersymmetric partition functions (2013, background): “(Various reductions from S 3 × S1 to squashed three-spheres were discussed in [44, 45, 54, 73, 74].”