Communications in Mathematical Physics

, Volume 304, Issue 3, pp 797–874 | Cite as

Elliptic Hypergeometry of Supersymmetric Dualities

  • V. P. Spiridonov
  • G. S. Vartanov


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 G 2 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.


Gauge Theory Gauge Group Supersymmetric Gauge Theory Superconformal Index Seiberg Duality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Bogoliubov Laboratory of Theoretical Physics, JINR, DubnaMoscow RegionRussia
  2. 2.Theory Division, INR RASMoscowRussia
  3. 3.Max-Planck-Institut für GravitationsphysikAlbert-Einstein-InstitutGolmGermany

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