$\mathcal{N}=2^{\ast }$ Schur indices

Abstract

We find closed-form expressions for the Schur indices of 4d $\mathcal{N}=2^{\ast }$ super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams associated with spectral zeta functions of an ideal Fermi-gas system. These functions are expressed in terms of the twisted Weierstrass functions, generating functions for quasi-Jacobi forms. The indices lie in the polynomial ring generated by the Kronecker theta function and the Weierstrass functions which contains the polynomial ring of the quasi-Jacobi forms. The grand canonical ensemble allows for another simple exact form of the indices as infinite series. In addition, we find that the unflavored Schur indices and their limits can be expressed in terms of several generating functions for combinatorial objects, including sum of triangular numbers, generalized sums of divisors and overpartitions.

61 pages

References in corpus (38)

• An Index for 4 dimensional Super Conformal Theories
• Infinite Chiral Symmetry in Four Dimensions
• Invasion of the Giant Gravitons from Anti-de Sitter Space
• Counting chiral primaries in N=1 d=4 superconformal field theories
• Modular invariance of trace functions in orbifold theory
• Large branes in AdS and their field theory dual
• Gauge Theories and Macdonald Polynomials
• SUSY and Goliath
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• S-duality and 2d Topological QFT
• Vertex operator algebras, Higgs branches, and modular differential equations
• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• Elliptic Genera and Applications to Mirror Symmetry
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• Infrared Computations of Defect Schur Indices
• Chiral algebra of Argyres-Douglas theory from M5 brane
• The exact Schur index of $\mathcal{N}=4$ SYM
• Line Operator Index on S1 $\times$ S3
• Conformal Manifolds in Four Dimensions and Chiral Algebras
• Schur index of the $\mathcal{N}=4$ $U(N)$ SYM via the AdS/CFT correspondence
• On a modular property of N=2 superconformal theories in four dimensions
• Schur correlation functions on $S^3\times S^1$
• SCFT/VOA correspondence via $\Omega$-deformation
• Torus n-Point Functions for $\mathbb{R}$-graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds
• The exact Schur index in closed form
• Exact Stringy Microstates from Gauge Theories
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• Gromov-Witten theory of elliptic fibrations: Jacobi forms and holomorphic anomaly equations
• Line defect Schur indices, Verlinde algebras and $U(1{)}_r$ fixed points
• Schur Indices of Class $\mathcal{S}$ and Quasimodular Forms
• Dualities of Corner Configurations and Supersymmetric Indices
• Modular Anomaly Equation for Schur Index of $\mathcal{N}=4$ Super-Yang-Mills
• Dualities and flavored indices of M2-brane SCFTs
• M2-branes and plane partitions
• SM(2,4k) fermionic characters and restricted jagged partitions
• On the definition and K-theory realization of a modular functor
• Partitions of large unbalanced bipartites

Cited by in corpus (10)

• Exact $\mathcal{N}=2^{\ast }$ Schur line defect correlators
• Large $N$ and large representations of Schur line defect correlators
• On Classification of Fermionic Rational Conformal Field Theories
• Excitations of bubbling geometries for line defects
• Giant graviton expansions and ETW brane
• ADHM Wilson line defect indices
• Asymptotic degeneracies of M2-brane SCFTs
• $\mathcal{N}=4$ line defect correlators of type BCD
• A landscape of 4d N=1 SCFTs with a=c
• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs