S-duality and 2d topological QFT

By Abhijit Gadde, E. Pomoni, L. Rastelli, Shlomo S. Razamat. 2009

304 citations recorded by the source corpus.

We study the superconformal index for the class of $$ \mathcal{N} = 2 $$ 4d superconformal field theories recently introduced by Gaiotto [1]. These theories are defined by compactifying the (2, 0) 6d theory on a Riemann surface with punctures. We interpret the index of the 4d theory associated to an n-punctured Riemann surface as the n-point correlation function of a 2d topological QFT living on the surface. Invariance of the index under generalized S-duality transformations (the mapping class group of the Riemann surface) translates into associativity of the operator algebra of the 2d TQFT. In the A1 case, for which the 4d SCFTs have a Lagrangian realization, the structure constants and metric of the 2d TQFT can be calculated explicitly in terms of elliptic gamma functions. Associativity then holds thanks to a remarkable symmetry of an elliptic hypergeometric beta integral, proved very recently by van de Bult [2].

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/044b5f595963cb799ee00f252065b36485376bff

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Citations in the corpus

On the superconformal index of Argyres–Douglas theories (2015, methodology): “Indeed, for a choice of C without irregular punctures, the superconformal index of TC is known to be equivalent to a correlator of a two-dimensional TQFT on C [18] (15)Here we use the normalization in which a fundamental hypermultiplet contributes kSU(2) = 2.”
A topologically twisted index for three-dimensional supersymmetric theories (2015, background): “A line of investigation we would like to suggest is about correspondences à la AGT [62, 63].”
Superconformal indices of three-dimensional theories related by mirror symmetry (2011, methodology): “Various developments and applications of this technique are described in [5, 6, 7, 8, 9].”
Elliptic Hypergeometry of Supersymmetric Dualities (2009, background): “Consider the following electric and magnetic theories SO(3) SU(3) U(1)R Q f f 2 3 SO(4) SU(3) U(1)R q f f 1 3 M 1 TS 4 3 As discussed by Intriligator and Seiberg [44, 45, 46] (see also [32]), the SO(3) Seiberg duality electric model becomes the SU(2) group N = 4 super-Yang-Mills theory in the infrar”
Gauge Theories and Macdonald Polynomials (2011, methodology): “(6)Note that while the fugacities (q, p) have exactly the same meaning in our previous papers [14, 23, 15], the fugacity t is different from the one introduced in [12] and used in [14, 23, 15].”
FROM 4d SUPERCONFORMAL INDICES TO 3d PARTITION FUNCTIONS (2011, background): “The relation between SCIs and the theory of elliptic hypergeometric functions was systematically investigated in [4, 5], where many new N = 1 dualities were discovered and a physical meaning of various mathematical properties of the elliptic hypergeometric integrals was recognized (see also [6, 7]).”
4d Index to 3d Index and 2d TQFT (2011, background): “When the 4d theory arises from the 6d (2, 0) theory on a punctured Riemann surface Σ, we conjecture the existence of a 2d topological quantum field theory (TQFT) on Σ whose correlation function coincides with the 4d index on S(1) × L(p, 1), generalizing a similar claim of [18, 19].”
Infinite Chiral Symmetry in Four Dimensions (2013, methodology): “This is very much in the spirit of [64] and [65], where the superconformal index and the symplectic holomorphic variety of the Higgs branch, respectively, were used to define a generalized TQFT via class S.”
N=1 theories of class S_k (2015, background): “The class S construction has an unexpected computational power, allowing for example to compute the superconformal index of all the four-dimensional class S theories, even though they might lack a Lagrangian description [10, 11, 12, 13], and relate S4 partition functions to 2d CFTs [14, 15].”
Bootstrapping the superconformal index with surface defects (2012, methodology): “Under a minimal set of assumptions, namely consistency of the 2d TQFT structure and knowledge of the index of free theories, we were then able to determine the index of a general theory of class S. 26The prescription of [23] gave divergent results for a small subclass of theories of class S, however”
Gauge Theories Labelled by Three-Manifolds (2011, methodology): “For example, on the gauge theory side one can associate either an equivariant partition function or an index (an analog of the elliptic genus) to the 3d N = 2 theory TM , by analogy with what was done in [3] or [41, 42] in the context of 4d N = 2 gauge theory.”
Reducing the 4d index to the S3 partition function (2011, methodology): “The expression above can be explicitly shown to exhibit this property [8].”
Schur indices, BPS particles, and Argyres-Douglas theories (2015, background): “It is related, in the context of class S theories, to q-deformed Yang-Mills theory [2, 3, 7–11], and most recently has made a prominent appearance in the connection of four-dimensional N = 2 theories to two-dimensional chiral algebras [12–15].”
Mirrors of 3d Sicilian theories (2010, background): “their gravity dual [4] and a IIB brane realization [5] have been found, their superconformal indices have been studied [6, 7], the theories have been extended to the case with orientifolds [8, 9], or lower N = 1 supersymmetry [10, 11], etc.”
Rigid supersymmetric theories in curved superspace (2011, methodology): “This fact has allowed [23,24,26-34] to compute Z”
The Hilbert series of the one instanton moduli space (2010, methodology): “The Hilbert series can be computed in analogy to the AGT relation [34, 35] as follows: g6−•−2−1(t) = ∫ dμSU(2)(z) g Irr E6 (t, z) gglue(t, z) g2−1(t, b, z) , (5.”