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This is a brief survey of the main results of the theory of elliptic hypergeometric functions--a
new class of special functions of mathematical physics. A proof is given of the most general …

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 …

The Schur limit of the superconformal index of a four-dimensional N= 2 superconformal field
theory encodes rich physical information about the protected spectrum of the theory. For a …

A bstract We construct classes of\(\mathcal {N}= 1\) superconformal theories elements of
which are labeled by punctured Riemann surfaces. Degenerations of the surfaces …

We give a full list of known N= 1 supersymmetric quantum field theories related by the
Seiberg electric-magnetic duality conjectures for SU (N), SP (2 N) and G 2 gauge groups …

A bstract We propose an explicit description of “duality walls” which encode at low energy
the global symmetry enhancement expected in the UV completion of certain five …

A bstract We study the geometry of 4d\(\mathcal {N}= 1\) SCFT's arising from
compactification of 6d (1, 0) SCFT's on a Riemann surface. We show that the conformal …

We derive an integral representation for the superconformal index of the strongly-
coupled\(\mathcal {N}= 2\) superconformal field theory with E 6 flavor symmetry. The explicit …

A bstract We discuss the four dimensional models obtained by compactifying a single M5
brane probing DN singularity (minimal D-type (1, 0) conformal matter in six dimensions) on a …