Defects, modular differential equations, and free field realization of N = 4 VOAs

Abstract

For all 4d $\mathcal{N}=4$ SYM theories with simple gauge groups $G$, we show that the residues of the integrands in the $\mathcal{N}=4$ Schur indices, which are related to Gukov-Witten type surface defects in the theories, equal the vacuum characters of rank$G$ copies of $bc\beta \gamma$ systems that provide the free field realization of associated $\mathcal{N}=4$ VOAs. This result predicts that these residues, as module characters, are additional solutions to the flavored modular differential equations satisfied by the original Schur index. The prediction is verified in the $G=SU(2)$ case, where an additional logarithmic solution is constructed.

References in corpus (28)

• Infinite Chiral Symmetry in Four Dimensions
• Bootstrapping the superconformal index with surface defects
• Schur Indices, BPS Particles, and Argyres-Douglas Theories
• Vertex operator algebras, Higgs branches, and modular differential equations
• Chiral algebras of class S
• Surface Defects and Chiral Algebras
• Infrared Computations of Defect Schur Indices
• Vertex operator algebras of Argyres-Douglas theories from M5-branes
• Chiral Algebras for Trinion Theories
• VOAs labelled by complex reflection groups and 4d SCFTs
• Exact results for supersymmetric abelian vortex loops in 2+1 dimensions
• Modular differential equations and null vectors
• Superconformal surfaces in four dimensions
• $\mathcal{N}=2$ central charge bounds from $2d$ chiral algebras
• Residues, modularity, and the Cardy limit of the 4d $\mathcal{N}=4$ superconformal index
• Free Field Realizations from the Higgs Branch
• Torus n-Point Functions for $\mathbb{R}$-graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds
• Schur correlation functions on $S^3\times S^1$
• Chiral Algebras, Localization and Surface Defects
• Ghost Systems: A Vertex Algebra Point of View
• Flavor symmetries and unitarity bounds in $\mathcal{N}=2$ SCFTs
• VOAs and rank-two instanton SCFTs
• On the Correspondence between Surface Operators in Argyres-Douglas Theories and Modules of Chiral Algebra
• Supersymmetric vortex defects in two dimensions
• A geometric free field realisation for the genus-two class $\mathcal{S}$ theory of type ${\mathfrak{a}}_1$
• The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
• Deformation quantizations from vertex operator algebras
• Modular differential equations for torus one-point functions

Cited by in corpus (4)

• The exact Schur index in closed form
• Surface defects, flavored modular differential equations and modularity
• On Classification of Fermionic Rational Conformal Field Theories
• 2d dualities from 4d