q-Virasoro/W algebra at root of unity and parafermions

  title={q-Virasoro/W algebra at root of unity and parafermions},
  author={Hiroshi Itoyama and T Oota and R. Yoshioka},
  journal={Nuclear Physics},

Figures from this paper

Virasoro constraint for Uglov matrix model
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
Elliptic algebra, Frenkel-Kac construction and root of unity limit
We argue that the level-1 elliptic algebra Uq,p(g^) is a dynamical symmetry realized as a part of 2d/5d correspondence where the Drinfeld currents are the screening currents to the q-Virasoro/W block
Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence
In this paper, we consider the q→0 limit of the deformed Virasoro algebra and that of the level 1, 2 representation of the Ding-Iohara-Miki algebra. Moreover, 5D AGT correspondence in this limit is
q-Virasoro constraints in matrix models
A bstractThe Virasoro constraints play the important role in the study of matrix models and in understanding of the relation between matrix models and CFTs. Recently the localization calculations in
NSR singular vectors from Uglov polynomials
It was conjectured by Belavin et al. [J. High Energy Phys. 2013(3), 35] that bosonization of a singular vector (in the Neveu–Schwarz sector) of the [Formula: see text] super analog of the Virasoro
AGT correspondence: Ding–Iohara algebra at roots of unity and Lepowsky–Wilson construction
It was recently conjectured that the AGT correspondence between the U ( r ) ?> —instanton counting on R 4 / Z p ?> and the two-dimensional field theories with the conformal symmetry algebra  ( r , p
q-Vertex Operator from 5D Nekrasov Function
The five-dimensional AGT correspondence implies the connection between the q-deformed Virasoro block and the 5d Nekrasov partition function. In this paper, we determine a q-deformation of the
Twisted reduction of quiver W-algebras
We consider the $k$-twisted Nekrasov-Shatashvili limit (NS$_k$ limit) of 5d (K-theoretic) and 6d (elliptic) quiver gauge theory, where one of the multiplicative equivariant parameters is taken to be
The integral representation of solutions of KZ equation and a modification by $\mathcal{K}$ operator insertion
A root of unity limit of the $q$-deformed Virasoro algebra is considered. The $\widehat{sl}(2)_k$ current algebra and the integral formulas of the solutions of the KZ equations can be realized by the
Developments of theory of effective prepotential from extended Seiberg–Witten system and matrix models
This is a semi-pedagogical review of a medium size on the exact determination of and the role played by the low energy effective prepotential F in QFT with (broken) extended supersymmetry, which


q-Virasoro algebra at root of unity limit and 2d-4d connection
We propose a limiting procedure in which, starting from the q-lifted version (or K-theoretic five dimensional version) of the (W)AGT conjecture to be assumed, the Virasoro/W block is generated in the
The Deformed Virasoro Algebra at Roots of Unity
Abstract:We discuss some aspects of the representation theory of the deformed Virasoro algebra $\virpq$. In particular, we give a proof of the formula for the Kac determinant and then determine the
We discuss a realization of stress–tensor for parafermion theories following a construction for higher level affine algebras, based on the projection of the standard level-one bosonic realization on
Structure constants in the N=1 superoperator algebra
Ramond sector of super Liouville theory from instantons on an ALE space
Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories
The conjecture about the correspondence between instanton partition functions in theN = 2 SUSY Yang-Mills theory and conformal blocks of two-dimensi onal conformal field theories is extended to the
On AGT relation in the case of U(3)
Construction of Gaiotto states with fundamental multiplets through degenerate DAHA
A bstractWe construct Gaiotto states with fundamental multiplets in SU(N ) gauge theories, in terms of the orthonormal basis of spherical degenerate double affine Hecke algebra (SH in short), the