We define a refined topological vertex which depends in addition on a parameter, which
physically corresponds to extending the self-dual graviphoton field strength to a more …

Consider the $3 $-dimensional $\mathcal N= 4$ supersymmetric gauge theory associated
with a compact Lie group $ G $ and its quaternionic representation $\mathbf M $. Physicists …

We study an analog of the AGT (Alday-Gaiotto-Tachikawa) relation in five dimensions. We
conjecture that the instanton partition function of 5D\(\mathcal {N}= 1\) pure SU (2) gauge …

A bstract We study various non-perturbative approaches to the quantization of the Seiberg-
Witten curve of\(\mathcal {N}\)= 2, SU (2) super Yang-Mills theory, which is closely related to …

In this paper, provide a survey of recent studies of supergroup gauge theory. We first discuss
the supermatrix model as a zero-dimensional toy model of supergroup gauge theory and its …

The simplest non-trivial 5d superconformal field theories (SCFT) are the famous rank-one
theories with $ E_n $ flavour symmetry. We study their $ U $-plane, which is the one …

In theories with extended supersymmetry the protected observables of UV superconformal
fixed points are found in a number of contexts to be encoded in the BPS solitons along an IR …

A bstract The moduli space of instantons on ℂ 2 for any simple gauge group is studied using
the Coulomb branch of\(\mathcal {N}= 4\) gauge theories in three dimensions. For a given …

A bstract We establish the equivalence between the refined topological vertex of Iqbal-
Kozcaz-Vafa and a certain representation theory of the quantum algebra of type W 1+∞ …

It has been argued that Nekrasov's partition function gives the generating function of refined
BPS state counting in the compactification of M theory on local Calabi–Yau spaces. We …