Quantum groups and quantum cohomology

D Maulik, A Okounkov - arxiv preprint arxiv:1211.1287, 2012 - arxiv.org
In this paper, we study the classical and quantum equivariant cohomology of Nakajima
quiver varieties for a general quiver Q. Using a geometric R-matrix formalism, we construct a …

M-strings

B Haghighat, A Iqbal, C Kozçaz, G Lockhart… - … in Mathematical Physics, 2015 - Springer
M2 branes suspended between adjacent parallel M5 branes lead to light strings, the 'M-
strings'. In this paper we compute the elliptic genus of M-strings, twisted by maximally …

Quantum geometry and quiver gauge theories

N Nekrasov, V Pestun, S Shatashvili - Communications in Mathematical …, 2018 - Springer
We study macroscopically two dimensional N=(2, 2) N=(2, 2) supersymmetric gauge
theories constructed by compactifying the quiver gauge theories with eight supercharges on …

Quantum difference equation for Nakajima varieties

A Okounkov, A Smirnov - Inventiones mathematicae, 2022 - Springer
For an arbitrary Nakajima quiver variety X, we construct an analog of the quantum dynamical
Weyl group acting in its equivariant K-theory. The correct generalization of the Weyl group …

Quiver Yangian and supersymmetric quantum mechanics

D Galakhov, M Yamazaki - Communications in Mathematical Physics, 2022 - Springer
The statistical model of crystal melting represents BPS configurations of D-branes on a toric
Calabi–Yau three-fold. Recently it has been noticed that an infinite-dimensional algebra, the …

Toroidal and elliptic quiver BPS algebras and beyond

D Galakhov, W Li, M Yamazaki - Journal of High Energy Physics, 2022 - Springer
A bstract The quiver Yangian, an infinite-dimensional algebra introduced recently in [1], is
the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We …

Explicit examples of DIM constraints for network matrix models

H Awata, H Kanno, T Matsumoto, A Mironov… - Journal of High Energy …, 2016 - Springer
A bstract Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov
functions for SYM theories in different dimensions, are all incorporated into network matrix …

-algebra modules, free fields, and Gukov-Witten defects

T Procházka, M Rapčák - Journal of High Energy Physics, 2019 - Springer
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 …

Liouville reflection operator, affine Yangian and Bethe ansatz

A Litvinov, I Vilkoviskiy - Journal of High Energy Physics, 2020 - Springer
A bstract In these notes we study integrable structure of conformal field theory by means of
Liouville reflection operator/Maulik Okounkov R-matrix. We discuss relation between RLL …

(p, q)-webs of DIM representations, 5d instanton partition functions and qq-characters

JE Bourgine, M Fukuda, K Harada, Y Matsuo… - Journal of High Energy …, 2017 - Springer
A bstract Instanton partition functions of\(\mathcal {N}= 1\) 5d Super Yang-Mills reduced on S
1 can be engineered in type IIB string theory from the (p, q)-branes web diagram. To this …