Derives a new basic hypergeometric beta integral identity from supersymmetric partition function equality on RP² × S¹ that does not arise as a degeneration of the lens elliptic beta integral.
A new pentagon identity for the tetrahedron index
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abstract
Recently Kashaev, Luo and Vartanov, using the reduction from a four-dimensional superconformal index to a three-dimensional partition function, found a pentagon identity for a special combination of hyperbolic Gamma functions. Following their idea we have obtained a new pentagon identity for a certain combination of so-called tetrahedron indices arising from the equality of superconformal indices of dual three-dimensional N=2 supersymmetric theories and give a mathematical proof of it.
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New Beta Integral from Supersymmetric Gauge Theory on Projective Space
Derives a new basic hypergeometric beta integral identity from supersymmetric partition function equality on RP² × S¹ that does not arise as a degeneration of the lens elliptic beta integral.