VOAs and rank-two instanton SCFTs

Abstract

We analyze the N=2 superconformal field theories that arise when a pair of D3-branes probe an F-theory singularity from the perspective of the associated vertex operator algebra. We identify these vertex operator algebras for all cases; we find that they have a completely uniform description, parameterized by the dual Coxeter number of the corresponding global symmetry group. We further present free field realizations for these algebras in the style of recent work by three of the authors. These realizations transparently reflect the algebraic structure of the Higgs branches of these theories. We find fourth-order linear modular differential equations for the vacuum characters/Schur indices of these theories, which are again uniform across the full family of theories and parameterized by the dual Coxeter number. We comment briefly on expectations for the still higher-rank cases.

arXiv comment30 pages; v2: minor typos corrected, published version

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• Towards a classification of rank $r$ $\mathcal{N}=2$ SCFTs Part II: special Kahler stratification of the Coulomb branch
• Magnetic quivers for rank 2 theories
• Argyres-Douglas Theories in Class S Without Irregularity
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• Higgs, Coulomb, and Hall-Littlewood
• On the compactification of 5d theories to 4d
• 3d mirrors of the circle reduction of twisted $A_{2N}$ theories of class $\mathsf{S}$
• Hecke Relations, Cosets and the Classification of 2d RCFTs
• Bootstrapping Coulomb and Higgs branch operators
• A geometric free field realisation for the genus-two class $\mathcal{S}$ theory of type ${\mathfrak{a}}_1$
• Defects, modular differential equations, and free field realization of N = 4 VOAs
• A new rank-2 Argyres-Douglas theory
• A tale of 2-groups: D${}_p$(USp(2N)) theories
• The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
• Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal{N}=4$ non-Abelian quiver gauge theories
• Free field realisation and the chiral universal centraliser
• Twisted chiral algebras of class $\mathcal{S}$ and mixed Feigin-Frenkel gluing
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories