Elliptic Hypergeometry of Supersymmetric Dualities

By V. Spiridonov, G. Vartanov. 2009

225 citations recorded by the source corpus.

We give a full list of known $${\mathcal{N}=1}$$ supersymmetric quantum field theories related by the Seiberg electric-magnetic duality conjectures for SU(N), SP(2N) and G2 gauge groups. Many of the presented dualities are new, not considered earlier in the literature. For all these theories we construct superconformal indices and express them in terms of elliptic hypergeometric integrals. This gives a systematic extension of the related Römelsberger and Dolan-Osborn results. Equality of indices in dual theories leads to various identities for elliptic hypergeometric integrals. About half of them were proven earlier, and another half represents new challenging conjectures. In particular, we conjecture a dozen new elliptic beta integrals on root systems extending the univariate elliptic beta integral discovered by the first author.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a8623748481e3a291ddb7b428463a0fa2aeac59f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Nuclear and High Energy Physics

Citations in the corpus

The geometry of supersymmetric partition functions (2013, background): “Explicit computations of the index (see for instance [33-36]) give rise to a class of special functions that has recently been studied in the mathematical literature (see for instance [37-39,34-36] and references therein).”
Gauge Theories and Macdonald Polynomials (2011, background): “ by Romelsberger [13, 17] and recently revisited with more rigor in [18]. Following the seminal work of Dolan and Osborn [19] there have been many checks and implications of this conjecture, see e.g. [20, 21, 22, 23, 24, 25]. 4In particular in [16] certain overall normalization factors were determin”
3d dualities from 4d dualities (2013, background): “ion function on a Euclidean S3 ×S1 which is renormalization-group invariant [12,13], and should thus be the same in any pair of theories that are IR-dual; this was veriﬁed explicitly in many examples [14, 15, 16, 17, 18, 19]. This supersymmetric partition function depends on the ratio of the radii o”
N=1 theories of class S_k (2015, background): “The index of this duality was discussed in [62].”
FROM 4d SUPERCONFORMAL INDICES TO 3d PARTITION FUNCTIONS (2011, background): “Naturally, using the connection between SCIs of four-dimensional field theories and elliptic hypergeometric integrals, in [5] it was proposed that SCIs themselves have an added interpretation in terms of relativistic Calogero-Sutherland models.”
Reducing the 4d index to the S3 partition function (2011, methodology): “of 4d gauge theories [1, 2] and the partition function of supersymmetric gauge theories on S3 [3, 4], are the main focus of this note. The superconformal index of N = 1 IR ﬁxed points was computed in [5, 6, 7], there it served as a check of Seiberg duality. The indices of N = 4 SYM and type IIB supe”
Superconformal indices of three-dimensional theories related by mirror symmetry (2011, methodology): “The Nf → Nf − 1 reduction in SCIs is realized similar to the 4d indices case [6].”
Relation between the 4d superconformal index and the S3 partition function (2011, methodology): “This quantity is exactly calculable, and is conveniently used as a tool to check Seiberg-duality[15, 16, 17, 18] and AdS5/CFT4[13, 19, 20, 21, 22].”
Rigid supersymmetric theories in curved superspace (2011, methodology): “This fact has allowed [23,24,26-34] to compute Z”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “ xqq;q), with e p q) the standard elliptic gamma function. { 8 { This beautiful result has led to some interesting lines of research linking indices to more formal mathematical constructions|see e.g. [34, 36, 37, 38, 39]. The A-model of a given N= 1 gauge theory is a topological eld theory, and it i”
Supersymmetry on curved spaces and holography (2012, background): “For the physicist after the mid-90ies an almost trivial thing, identifying the index for two Seiberg dual phases of the same theory turns out to be at the edge of knowledge for the mathematicians [24, 25].”
Localization on Hopf surfaces (2014, methodology): “The supersymmetric index was introduced in [11, 12, 13] in the context of superconformal field theories, and has been used in [14, 15, 16, 17] (and many others) to test non-perturbative dualities.”
The superconformal index of the E6 SCFT (2010, unknown): “he two SU(3) factors in the 7This identity was extensively used in [16] to show that certain theories related by Seiberg duality have equal superconformal indices [21]. In this context the authors of [22, 23] applied the elliptic hypergeometric techniques to a large class of Seiberg dualities. – 10 ”