Yang–Mills theories in four space–time dimensions possess a hidden symmetry which does
not exhibit itself as a symmetry of classical Lagrangians but is only revealed on the quantum …

We study the N= 2 four-dimensional superconformal index in various interesting limits, such
that only states annihilated by more than one supercharge contribute. Extrapolating from the …

A bstract The analytic properties of the\(\mathcal {N}= 2\) superconformal index are given a
physical interpretation in terms of certain BPS surface defects, which arise as the IR limit of …

In the case of SU (2), associated by the AGT relation to the 2d Liouville theory, the Seiberg-
Witten prepotential is constructed from the Bohr-Sommerfeld periods of 1d sine-Gordon …

We compute the prepotential of Script N= 2 supersymmetric gauge theories in four
dimensions obtained by toroidal compactifications of gauge theories from 6 dimensions, as …

A bstract We study the Nekrasov partition function of the five dimensional U (N) gauge theory
with maximal supersymmetry on ℝ 4× S 1 in the presence of codimension two defects. The …

Even though matrix model partition functions do not exhaust the entire set of τ-functions
relevant for string theory, they seem to be elementary building blocks for many others and …

We give a concise summary of the impressive recent development unifying a number of
different fundamental subjects. The quiver Nekrasov functions (generalized hypergeometric …

A bstract We review some of the properties of 3d\(\mathcal {N}= 4\) theories obtained by
dimensionally reducing theories of class\(\mathcal {S}\). We study 3d partition functions, and …

A matrix model approach to proof of the AGT relation is briefly reviewed. It starts from the
substitution of conformal blocks by the Dotsenko–Fateev β-ensemble averages and …