Quantum Reduction for Affine Superalgebras

Abstract

We extend the homological method of quantization of generalized Drinfeld--Sokolov reductions to affine superalgebras. This leads, in particular, to a unified representation theory of superconformal algebras.

33 pages, LaTex

References in corpus (4)

• Field Algebras
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• Heisenberg and Modular Invariance of N=2 Conformal Field Theory
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Cited by in corpus (118)

• Finite vs. affine W-algebras
• Modular Data and Verlinde Formulae for Fractional Level WZW Models I
• W-algebras as coset vertex algebras
• Tensor categories for vertex operator superalgebra extensions
• Modular Data and Verlinde Formulae for Fractional Level WZW Models II
• Rationality of W-algebras: principal nilpotent cases
• Representations of shifted Yangians and finite W-algebras
• Coset Constructions of Logarithmic (1,p)-Models
• Cosets of affine vertex algebras inside larger structures
• Joseph ideals and lisse minimal W-algebras
• Webs of W-algebras
• Plane partitions with a "pit": generating functions and representation theory
• Conformal embeddings of affine vertex algebras in minimal $W$-algebras I: structural results
• Trialities of $\mathcal{W}$-algebras
• Duality of subregular W-algebras and principal W-superalgebras
• Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
• Invariant Differential Operators for Non-Compact Lie Algebras Parabolically Related to Conformal Lie Algebras
• Rationality of Bershadsky-Polyakov vertex algebras
• Orbifolds and cosets of minimal $\mathcal{W}$-algebras
• Screening operators for W-algebras
• Explicit generators in rectangular affine W-algebras of type A
• Classification of supersymmetries
• Associated varieties of modules over Kac-Moody algebras and $C_2$-cofiniteness of W-algebras
• Universal two-parameter ${\mathcal{W}}_{\infty }$-algebra and vertex algebras of type $\mathcal{W}(2,3,\dots ,N)$
• Tensor categories of affine Lie algebras beyond admissible levels
• A realisation of the Bershadsky--Polyakov algebras and their relaxed modules
• Schur sector of Argyres-Douglas theory and $W$-algebra
• Nilpotent orbits and finite W-algebras
• Universal two-parameter even spin ${\mathcal{W}}_{\infty }$-algebra
• Representation theory of W-algebras, II: Ramond twisted representations
• Rationality and Fusion Rules of Exceptional W-Algebras
• Affine Super Yangians and Rectangular $W$-superalgebras
• Trialities of orthosymplectic $\mathcal{W}$-algebras
• Cosets of Bershadsky-Polyakov algebras and rational $\mathcal{W}$-algebras of type $A$
• Two-sided BGG resolutions of admissible representations
• Invariant subalgebras of affine vertex algebras
• W-algebras and surface operators in N=2 gauge theories
• Vertex Algebras at the Corner
• An application of collapsing levels to the representation theory of affine vertex algebras
• Unitary and non-unitary $N=2$ minimal models
• Cosets of the ${\mathcal{W}}^k({\mathfrak{sl}}_4,f_{\text{subreg}})$-algebra
• Localization of affine W-algebras
• Haploid algebras in $C^{\ast }$-tensor categories and the Schellekens list
• Fusion rules for the logarithmic $N=1$ superconformal minimal models I: the Neveu-Schwarz sector
• Fusion rules for the logarithmic $N=1$ superconformal minimal models II: including the Ramond sector
• Screening operators and Parabolic inductions for Affine W-algebras (with an appendix by Shigenori Nakatsuka)
• Admissible-level ${\mathfrak{sl}}_3$ minimal models
• Correspondences among CFTs with different W-algebra symmetry
• W-algebras at the critical level
• Classifying relaxed highest-weight modules for admissible-level Bershadsky-Polyakov algebras
• Dirac operators and the Very Strange Formula for Lie superalgebras
• On classical finite and affine W-algebras
• Chiral Homology of elliptic curves and the Zhu algebra
• Modularity of Bershadsky-Polyakov minimal models
• Correspondences of categories for subregular W-algebras and principal W-superalgebras
• Supersymmetric W-algebras
• Higher rank isomonodromic deformations and W-algebras
• Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras
• Subregular W-algebras of type A
• Moeglin's theorem and Goldie rank polynomials in Cartan type A
• Good Gradings of Simple Lie Algebras
• Rationality of the exceptional W-algebras ${\mathcal{W}}_k({\mathfrak{sp}}_4,f_{subreg})$ associated with subregular nilpotent elements of ${\mathfrak{sp}}_4$
• Modularity of Relatively Rational Vertex Algebras and Fusion Rules of Principal Affine W-Algebras
• Minimal W-superalgebras and modular representations of basic Lie superalgebras
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• A commutant realization of W^(2)_n at critical level
• Affine Laumon spaces and iterated W-algebras
• Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras
• Modular invariant representations of the $\mathcal{N}=2$ superconformal algebra
• Kazama-Suzuki coset construction and its inverse
• On low rank 4d $\mathcal{N}=2$ SCFTs
• Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal{N}=4$ non-Abelian quiver gauge theories
• Unitarity of minimal $W$-algebras and their representations I
• Strong generators of the subregular W-algebra and combinatorial description at critical level
• Characters of representations of affine Kac-Moody Lie algebras at the critical level
• Twisted logarithmic modules of free field algebras
• On Miura maps for W-superalgebras
• Ramond sector of superconformal algebras via quantum reduction
• Reduction by stages for finite W-algebras
• Snowflake modules and Enright functor for Kac-Moody superalgebras
• Quasi-lisse extension of affine ${\mathfrak{sl}}_2$ à la Feigin--Tipunin
• Simplicity of vacuum modules and associated varieties
• On rationality for $C_2$-cofinite vertex operator algebras
• On free field realization of quantum affine $W$-algebras
• Generators of Supersymmetric Classical $W$-algebras
• Ordinary modules for vertex algebras of ${\mathfrak{osp}}_{1|2n}$
• On the structure of W-algebras in type A
• Dirac reductions and Classical W-algebras
• Orbifolds of Gaiotto-Rapčák $Y$-algebras
• Rationality of vertex operator superalgebras with rational conformal weights
• Gelfand-Kirillov Conjecture and Harish-Chandra Modules for Finite W-Algebras
• Ito's conjecture and the coset construction for ${\mathcal{W}}^k(\mathfrak{sl}(3|2))$
• Center of affine ${\mathfrak{sl}}_{2|1}$ at the critical level
• $N=1$ super Virasoro tensor categories
• Quasi-Characters in $\widehat{su(2)}$ Current Algebra at Fractional Levels
• Orthosymplectic Feigin-Semikhatov duality
• $W$-algebras associated with centralizers in type $A$
• On finite dimensional representations of finite W-superalgebras
• Generalized Wick theorems in conformal field theory and the Borcherds identity
• A commutant realization of Odake's algebra
• Functorial constructions related to double Poisson vertex algebras
• Unitarity of minimal $W$-algebras and their representations II: Ramond sector
• On rationality of W-algebras
• Classification of finite-growth general Kac-Moody superalgebras
• Admissible pairs of a complex simple Lie algebra and finite W-algebras
• Connecting affine $\mathcal{W}$-algebras: A case study on ${\mathfrak{sl}}_4$
• Duality via convolution of W-algebras
• Twisted Affine Yangian and Rectangular $W$-algebra of type $D$
• Generalized finite and affine $W$-algebras in type $A$
• Conformal nets from minimal W-algebras
• Bosonic Ghost Correlators: A Case Study
• Relaxed and logarithmic modules of $\widehat{{\mathfrak{sl}}_3}$
• On good Z-gradings of basic Lie superalgebras
• Unitarity of minimal $W$-algebras
• Classification of Invariant Differential Operators for Non-Compact Lie Algebras via Parabolic Relations
• Feigin-Semikhatov conjecture and related topics
• Yangians vs minimal W-algebras: a surprizing coincidence
• Associated varieties of simple affine VOAs $L_k(s{l}_3)$ and $W$-algebras $W_k(s{l}_3,f)$