Related papers: Solving q-Virasoro constraints
The q-Painleve equation, satisfied by the Fourier transform of the q-Virasoro conformal blocks at c=1, is interpreted as a reformulation of the string equation and two other Virasoro constraints in the $5d$ Dotsenko-Fateev matrix model.
We study solutions of the reflection equation related to the quantum affine algebra $U_q(\widehat{sl_n})$. First, we explain how to construct a family of stochastic integrable vertex models with fixed boundary conditions. Then, we construct…
We investigate the central extensions of the q-deformed (classical and quantum) Virasoro algebras constructed from the elliptic quantum algebra A_{q,p}[sl(N)_c]. After establishing the expressions of the cocycle conditions, we solve them,…
Some issues in the loop variable renormalization group approach to gauge invariant equations for the free fields of the open string are discussed. It had been shown in an earlier paper that this leads to a simple form of the gauge…
Models which include domain constraints occur in myriad contexts such as econometrics, genomics, and environmetrics, though simulating from constrained distributions can be computationally expensive. In particular, repeated sampling from…
Based on the quantum superspace construction of $q$-deformed algebra, we discuss a supersymmetric extension of the deformed Virasoro algebra, which is a subset of the $q$-$W_{\infty}$ algebra recently appeared in the context of…
In this paper, we study the tensor products of irreducible highest weight modules with irreducible loop modules over the affine-Virasoro algebra with aid of the ``shifting technique" established for the Virasoro algebra in [H. Chen, X. Guo,…
We study the root of unity limit of $(\textbf{q}, \textbf{t})$-deformed Virasoro matrix models, for which we call the resulting model Uglov matrix model. We derive the associated Virasoro constraints on the partition function and find…
We investigate the free fields realization of the twisted Heisenberg-Virasoro algebra $\mathcal{H}$ at level zero. We completely describe the structure of the associated Fock representations. Using vertex-algebraic methods and screening…
For q generic or a primitive l-th root of unity, q-Witt algebras are described by means of q-divided power algebras. The structure of the universal q-central extension of the q-Witt algebra, the q-Virasoro algebra, is also determined. q-Lie…
A new approach to the theory of polynomial solutions of q - difference equations is proposed. The approach is based on the representation theory of simple Lie algebras and their q - deformations and is presented here for U_q(sl(n)). First a…
We derive a set of integral equations of the TBA type for the generalized cusp anomalous dimension, or the quark antiquark potential on the three sphere, as a function of the angles. We do this by considering a family of local operators on…
The aim of the paper is to study modules for the twisted Heisenberg-Virasoro algebra $\mathcal H$ at level zero as modules for the $W(2,2)$-algebra by using construction from [J. Pure Appl. Algebra 219 (2015), 4322-4342, arXiv:1405.1707].…
Tensor product of highest weight modules and intermediate modules for Virasoro algebra have been studied around 1997. Since then the irreducibility problem for tensor product of modules is open. We consider the loop-Virasoro algebra $Vir…
The spectrum of conformal weights for the CFT describing the two-dimensional critical $Q$-state Potts model (or its close cousin, the dense loop model) has been known for more than 30 years. However, the exact nature of the corresponding…
How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with…
We describe the structure of the irreducible highest weight modules for the twisted Heisenberg-Virasoro Lie algebra at level zero. We prove that such a module is either isomorphic to a Verma module or to a quotient of two Verma modules.
Lie algebra valued equations translating the integrability of a general two-dimensional Wess-Zumino-Witten model are given. We found simple solutions to these equations and identified three types of new integrable non-linear sigma models.…
We show that the partition function of the super eigenvalue model satisfies an infinite set of constraints with even spins $s=4,6,\cdots,\infty$. These constraints are associated with half of the bosonic generators of the super $\left(…
In this paper, we follow a Bootstrap-like approach to determine the most restricted form the finiteness constraint $\mathcal{F}(q,g,h,\kappa)$, which relates the four parameters of $\mathcal{N}=1$ Leigh-Strassler (LS) deformed models, by…