# 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}
}
• Published 1 October 2018
• Physics
• Letters in Mathematical Physics
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
• Physics
Journal 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
• Mathematics
Letters 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
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
• A. Morozov
• Physics
Journal 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
• Physics
Journal 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

## References

SHOWING 1-10 OF 33 REFERENCES
q-Virasoro Modular Double and 3d Partition Functions
• Mathematics
• 2016
We study partition functions of 3d $${\mathcal{N}=2}$$N=2$${{\rm U}(N)}$$U(N) gauge theories on compact manifolds which are S1 fibrations over S2. We show that the partition functions are free field
Holomorphic blocks in three dimensions
• Mathematics
• 2012
A bstractWe decompose sphere partition functions and indices of three-dimensional N$$\mathcal{N}$$ = 2 gauge theories into a sum of products involving a universal set of “holomorphic blocks”. The
Gauge/Liouville Triality
• Physics
• 2013
Conformal blocks of Liouville theory have a Coulomb-gas representation as Dotsenko-Fateev (DF) integrals over the positions of screening charges. For q-deformed Liouville, the conformal blocks on a
Symplectic invariants, Virasoro constraints and Givental decomposition
Following the works of Alexandrov, Mironov and Morozov, we show that the symplectic invariants of \cite{EOinvariants} built from a given spectral curve satisfy a set of Virasoro constraints
Virasoro action on Schur function expansions, Skew Young tableaux, and random walks
It is known that some matrix integrals over U(n) satisfy an sl(2,R)-algebra of Virasoro constraints. Acting with these Virasoro generators on 2-dimensional Schur function expansions leads to
Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
• Mathematics
• 2016
We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well as averages of Schur
Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions
A bstractWe study five dimensional AGT correspondence by means of the q-deformed beta-ensemble technique. We provide a special basis of states in the q-deformed CFT Hilbert space consisting of
Topological expansion of the β-ensemble model and quantum algebraic geometry in the sectorwise approach
• Mathematics
• 2011
AbstractWe construct the solution of the loop equations of the β-ensemble model in a form analogous to the solution in the case of the Hermitian matrices β = 1. The solution for β = 1 is expressed in