Elliptic Hypergeometry of Supersymmetric Dualities
Oct, 200980 pages
Published in:
- Commun.Math.Phys. 304 (2011) 797-874
e-Print:
- 0910.5944 [hep-th]
Report number:
- AEI-2009-106
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Abstract: (arXiv)
We give a full list of known supersymmetric quantum field theories related by the Seiberg electric-magnetic duality conjectures for and 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 Romelsberger 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.Note:
- 70 pages, published version
- supersymmetry: duality
- gauge field theory: SU(N)
- gauge field theory: Sp(N)
- gauge field theory: G(2)
- algebra: conformal
- index theorem
- anomaly
- algebraic geometry
- analytic properties
- mathematical methods
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