# Solving q-Virasoro constraints

@article{Lodin2019SolvingQC, title={Solving q-Virasoro constraints}, author={Rebecca Lodin and Aleksandr Popolitov and Shamil Shakirov and Maxim Zabzine}, journal={Letters in Mathematical Physics}, year={2019}, volume={110}, pages={179-210} }

AbstractWe show how q-Virasoro constraints can be derived for a large class of (q, t)-deformed eigenvalue matrix models by an elementary trick of inserting certain q-difference operators under the integral, in complete analogy with full-derivative insertions for $$\beta $$β-ensembles. From free field point of view, the models considered have zero momentum of the highest weight, which leads to an extra constraint $$T_{-1} \mathcal {Z} = 0$$T-1Z=0. We then show how to solve these q-Virasoro…

## 23 Citations

Exact SUSY Wilson loops on S3 from q-Virasoro constraints

- PhysicsJournal of High Energy Physics
- 2019

Abstract
Using the ideas from the BPS/CFT correspondence, we give an explicit recur- sive formula for computing supersymmetric Wilson loop averages in 3d
$$ \mathcal{N} $$
N
= 2…

On refined Chern–Simons and refined ABJ matrix models

- MathematicsLetters in Mathematical Physics
- 2022

We consider the matrix model of U(N) refined Chern–Simons theory on $$S^3$$
S
3
for the unknot. We derive a q-difference operator whose insertion in the matrix integral reproduces an infinite…

On matrix models and their q-deformations

- Mathematics
- 2020

Motivated by the BPS/CFT correspondence, we explore the similarities between the classical $\beta$-deformed Hermitean matrix model and the $q$-deformed matrix models associated to 3d $\mathcal{N}=2$…

BPS Quivers of Five-Dimensional SCFTs, Topological Strings and q-Painlevé Equations

- Mathematics
- 2020

We study the discrete flows generated by the symmetry group of the BPS quivers for Calabi-Yau geometries describing five dimensional superconformal quantum field theories on a circle. These flows…

Non-stationary difference equation for q-Virasoro conformal blocks

- Mathematics
- 2021

is a remarkable infinite-dimensional Lie algebra which arises [2] as the unique central extension of infinitesimal two-dimensional conformal transformations, and as such has natural and long known…

Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model

- Mathematics
- 2022

We consider supersymmetric surface defects in compactifications of the $6d$ minimal $(D_{N+3},D_{N+3})$ conformal matter theories on a punctured Riemann surface. For the case of $N=1$ such defects…

Quiver Wε1,ε2 algebras of 4d N = 2 gauge theories

- Mathematics
- 2020

We construct an ϵ-deformation of W algebras, corresponding to the additive version of quiver W q , t − 1 algebras which feature prominently in the 5D version of the BPS/CFT correspondence and refined…

A new kind of anomaly: on W-constraints for GKM

- PhysicsJournal of High Energy Physics
- 2021

Abstract
We look for the origins of the single equation, which is a peculiar combination of W-constrains, which provides the non-abelian W-representation for generalized Kontsevich model (GKM), i.e.…

Virasoro constraint for Uglov matrix model

- PhysicsJournal of High Energy Physics
- 2022

Abstract
We study the root of unity limit of (q,t)-deformed Virasoro matrix models, for which we call the resulting model Uglov matrix model. We derive the associated Virasoro constraints on the…

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