On a modular property of N=2 superconformal theories in four dimensions

Abstract

In this note we discuss several properties of the Schur index of N=2 superconformal theories in four dimensions. In particular, we study modular properties of this index under SL(2,Z) transformations of its parameters.

23 page, 2 figures

References in corpus (7)

• Mock Theta Functions
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• S-duality in N=2 supersymmetric gauge theories
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• Exploring Curved Superspace
• 4d partition function on S^1 x S^3 and 2d Yang-Mills with nonzero area

Cited by in corpus (28)

• Infinite Chiral Symmetry in Four Dimensions
• 3d dualities from 4d dualities
• Schur Indices, BPS Particles, and Argyres-Douglas Theories
• Vertex operator algebras, Higgs branches, and modular differential equations
• Infrared Computations of Defect Schur Indices
• Supersymmetric Casimir Energy and the Anomaly Polynomial
• Supersymmetric phases of 4d N=4 SYM at large N
• The exact Schur index of $\mathcal{N}=4$ SYM
• Higgs branch localization of $\mathcal{N}=1$ theories on $S^3\times S^1$
• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• Residues, modularity, and the Cardy limit of the 4d $\mathcal{N}=4$ superconformal index
• The $\mathcal{N}=2$ Schur index from free fermions
• The exact Schur index in closed form
• $\mathcal{N}=2^{\ast }$ Schur indices
• $c-a$ from the $N=1$ superconformal index
• Central charges from the $\mathcal{N}=1$ superconformal index
• The $\mathcal{N}=4$ Schur index with Polyakov loops
• Schur Indices of Class $\mathcal{S}$ and Quasimodular Forms
• Surface defects, flavored modular differential equations and modularity
• Modularity of supersymmetric partition functions
• On the N=2 superconformal index and eigenfunctions of the elliptic RS model
• Microscopic Entropy of AdS${}_3$ Black Holes Revisited
• Supersymmetric Casimir Energy and $\mathrm{SL}(3,\mathbb{Z})$ Transformations
• $\mathcal{N}=1$ conformal duals of gauged $E_n$ MN models
• Modularity and 4D-2D spectral equivalences for large-N gauge theories with adjoint matter
• A 4D-2D equivalence for large-N Yang-Mills theory
• Root of unity asymptotics for Schur indices of 4d Lagrangian theories
• Supersymmetric zeta functions and determinants