This is a review article on the quantum toroidal algebras, focusing on their roles in various
solvable structures of 2d conformal field theory, supersymmetric gauge theory, and string …

Starting with a gentle approach to the Alday–Gaiotto–Tachikawa (AGT) correspondence
from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on …

A bstract The relationship of two dimensional quantum field theory and isomonodromic
deformations of Fuchsian systems has a long history. Recently four-dimensional N= 2 gauge …

A bstract We explore the quantum algebraic formalism of the gauge origami system in ℂ 4,
where D2/D4/D6/D8-branes are present. We demonstrate that the contour integral formulas …

A bstract We propose a systematic approach to computing the BPS spectrum of any 5d/6d
supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory …

A bstract We associate vertex operator algebras to (p, q)-webs of interfaces in the
topologically twisted\(\mathcal {N}= 4\) super Yang-Mills theory. Y-algebras associated to …

A bstract We propose an interesting BPS/CFT correspondence playground: the correlation
function of two intersecting half-BPS surface defects in four-dimensional\(\mathcal {N}\)= 2 …

A bstract We study the structure of modules of corner vertex operator algebras arrising at
junctions of interfaces in\(\mathcal {N}= 4\) SYM. In most of the paper, we concentrate on …

A bstract We explore the difference Langlands correspondence using the four
dimensional\(\mathcal {N}\)= 2 super-QCD. Surface defects and surface observables play …

A bstract We describe the general strategy for lifting the Wess-Zumino-Witten model from the
level of one-loop Kac-Moody\({U} _q {\left (\widehat {\mathfrak {g}}\right)} _k\) to generic …