$q$-Virasoro/W Algebra at Root of Unity and Parafermions

Abstract

We demonstrate that the parafermions appear in the $r$-th root of unity limit of $q$-Virasoro/$W_n$ algebra. The proper value of the central charge of the coset model $\frac{\widehat{\mathfrak{sl}}(n{)}_r\oplus \widehat{\mathfrak{sl}}(n{)}_{m-n}}{\widehat{\mathfrak{sl}}(n{)}_{m-n+r}}$ is given from the parafermion construction of the block in the limit.

arXiv comment13 pages, 1 figure; v2: references added, minor corrections made

References in corpus (43)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT relation in the case of U(3)
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
• Quantum W-algebras and Elliptic Algebras
• Quantum $W_N$ Algebras and Macdonald Polynomials
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Para-Liouville/Toda central charges from M5-branes
• The Quiver Matrix Model and 2d-4d Conformal Connection
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• Five-dimensional AGT Relation and the Deformed beta-ensemble
• Non-Lagrangian Theories from Brane Junctions
• A direct proof of AGT conjecture at beta = 1
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories
• Instanton moduli spaces and bases in coset conformal field theory
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• 5D partition functions, q-Virasoro systems and integrable spin-chains
• Instantons on ALE spaces and Super Liouville Conformal Field Theories
• Instantons and 2d Superconformal field theory
• Finalizing the proof of AGT relations with the help of the generalized Jack polynomials
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• Yangian Gelfand-Zetlin Bases, gl(N)-Jack Polynomials and computation of Dynamical Correlation Functions in the Spin Calogero-Sutherland Model
• Ramond sector of super Liouville theory from instantons on an ALE space
• Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function
• Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity
• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• Generalized Jack polynomials and the AGT relations for the $SU(3)$ group
• Structure constants in the N=1 superoperator algebra
• 2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space
• Parafermionic Liouville field theory and instantons on ALE spaces
• An M-Theoretic Derivation of a 5d and 6d AGT Correspondence, and Relativistic and Elliptized Integrable Systems
• Coset conformal blocks and N=2 gauge theories
• The deformed Virasoro algebra at roots of unity
• The orthogonal eigenbasis and norms of eigenvectors in the Spin Calogero-Sutherland Model
• A twisted conformal field theory description of the Quantum Hall Effect
• Coset conformal field theory and instanton counting on C^2/Z_p
• Matching branches of non-perturbative conformal block at its singularity divisor
• Sress-Tensor for parafermions from the generalized Frenkel-Kac construction of affine algebra
• A stringy perspective on the quantum integrable model/gauge correspondence

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• Anomaly in RTT relation for DIM algebra and network matrix models
• A slow review of the AGT correspondence
• Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
• On elementary proof of AGT relations from six dimensions
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence
• $q$-Virasoro modular double and 3d partition functions
• Argyres-Douglas theories and Liouville Irregular States
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• q-Vertex Operator from 5D Nekrasov Function
• The integral representation of solutions of KZ equation and a modification by $\mathcal{K}$ operator insertion
• On generalized Macdonald polynomials
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• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Virasoro Constraint for Uglov Matrix Model
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• NSR singular vectors from Uglov polynomials
• On refined Chern-Simons and refined ABJ matrix models
• Direct Sum Structure of the Super Virasoro Algebra and a Fermion Algebra Arising from the Quantum Toroidal ${\mathfrak{gl}}_2$