On Irregular Singularity Wave Functions and Superconformal Indices

Abstract

We generalize, in a manifestly Weyl-invariant way, our previous expressions for irregular singularity wave functions in two-dimensional SU(2) q-deformed Yang-Mills theory to SU(N). As an application, we give closed-form expressions for the Schur indices of all (A_{N-1}, A_{N(n-1)-1}) Argyres-Douglas (AD) superconformal field theories (SCFTs), thus completing the computation of these quantities for the (A_N, A_M) SCFTs. With minimal effort, our wave functions also give new Schur indices of various infinite sets of "Type IV" AD theories. We explore the discrete symmetries of these indices and also show how highly intricate renormalization group (RG) flows from isolated theories and conformal manifolds in the ultraviolet to isolated theories and (products of) conformal manifolds in the infrared are encoded in these indices. We compare our flows with dimensionally reduced flows via a simple "monopole vev RG" formalism. Finally, since our expressions are given in terms of concise Lie algebra data, we speculate on extensions of our results that might be useful for probing the existence of hypothetical SCFTs based on other Lie algebras. We conclude with a discussion of some open problems.

34 pages, 2 figures

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Cited by in corpus (36)

• Vertex operator algebras, Higgs branches, and modular differential equations
• Lagrangians for generalized Argyres-Douglas theories
• Vertex operator algebras of Argyres-Douglas theories from M5-branes
• N=1 Lagrangians for generalized Argyres-Douglas theories
• Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6d $(2,0)$ theories
• Logarithmic W-algebras and Argyres-Douglas theories at higher rank
• A slow review of the AGT correspondence
• Nonunitary Lagrangians and unitary non-Lagrangian conformal field theories
• Chiral Algebras, Localization and Surface Defects
• The vertex algebras ${\mathcal{R}}^{(p)}$ and ${\mathcal{V}}^{(p)}$
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• Schur sector of Argyres-Douglas theory and $W$-algebra
• Rationalizing CFTs and Anyonic Imprints on Higgs Branches
• Braided Tensor Categories related to ${\mathcal{B}}_p$ Vertex Algebras
• On the chiral algebra of Argyres-Douglas theories and S-duality
• Three Dimensional Mirror Symmetry beyond $ADE$ quivers and Argyres-Douglas theories
• Four-dimensional Lens Space Index from Two-dimensional Chiral Algebra
• On the Correspondence between Surface Operators in Argyres-Douglas Theories and Modules of Chiral Algebra
• Line defect Schur indices, Verlinde algebras and $U(1{)}_r$ fixed points
• Vanishing OPE Coefficients in 4d N=2 SCFTs
• Surface defects, flavored modular differential equations and modularity
• Argyres-Douglas matter and S-duality: Part II
• Flowing from 16 to 32 Supercharges
• Notes on Integral Identities for 3d Supersymmetric Dualities
• On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories
• A tale of 2-groups: D${}_p$(USp(2N)) theories
• Testing Macdonald Index as a Refined Character of Chiral Algebra
• Closed form fermionic expressions for the Macdonald index
• An infrared bootstrap of the Schur index with surface defects
• W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branes
• Peculiar Index Relations, 2D TQFT, and Universality of SUSY Enhancement
• Orbifold Schur Index and IR formula
• 4d $\mathcal{N}=2$ SCFTs and lisse W-algebras
• A study of N =1 SCFT derived from N =2 SCFT: index and chiral ring
• A landscape of 4d N=1 SCFTs with a=c
• Vanishing short multiplets in rank one 4d/5d SCFTs