Supersymmetric zeta functions and determinants

Abstract

We define supersymmetric zeta functions and supersymmetric determinants, which can reveal spectral properties complementary to those captured by the supersymmetric indices. They play a crucial role in analyzing the Cardy-like behaviors of the supersymmetric indices and the supersymmetric Casimir energies associated with the supersymmetric partition functions. We investigate a variety of examples of the supersymmetric zeta functions and determinants for two-, four-, and six-dimensional supersymmetric field theories.

125 pages, 5 figures, v2: published version in JHEP

References in corpus (82)

• N=2 dualities
• An Index for 4 dimensional Super Conformal Theories
• Conformal collider physics: Energy and charge correlations
• Infinite Chiral Symmetry in Four Dimensions
• The Exact Superconformal R-Symmetry Maximizes a
• Counting chiral primaries in N=1 d=4 superconformal field theories
• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• Gauge Theories and Macdonald Polynomials
• Elliptic genera of 2d N=2 gauge theories
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• 6d Conformal Matter
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Sasaki-Einstein Manifolds and Volume Minimisation
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• The Geometric Dual of a-maximisation for Toric Sasaki-Einstein Manifolds
• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• Two-dimensional SCFTs from wrapped branes and c-extremization
• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
• General Argyres-Douglas Theory
• M5-branes from gauge theories on the 5-sphere
• Schur Indices, BPS Particles, and Argyres-Douglas Theories
• Anomaly polynomial of general 6d SCFTs
• Cardy Formulae for SUSY Theories in d=4 and d=6
• W Symmetry in six dimensions
• Exact two-dimensional superconformal R-symmetry and c-extremization
• Operator bases, $S$-matrices, and their partition functions
• Central charges of N=2 superconformal field theories in four dimensions
• Vertex operator algebras, Higgs branches, and modular differential equations
• Localization on Hopf surfaces
• On the Superconformal Index of Argyres-Douglas Theories
• GLSM's for gerbes (and other toric stacks)
• What Maxwell Theory in D<>4 teaches us about scale and conformal invariance
• La fonction Zeta de Riemann prend une infinite de valeurs irrationnelles aux entiers impairs
• String compactifications on Calabi-Yau stacks
• (0,2) Trialities
• The asymptotic growth of states of the 4d N=1 superconformal index
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• A 4d N=1 Cardy Formula
• Classification of Argyres-Douglas theories from M5 branes
• Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
• Perturbative partition function for a squashed S^5
• Infrared Computations of Defect Schur Indices
• Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS${}_5$ blackholes
• Vertex operator algebras of Argyres-Douglas theories from M5-branes
• EFT and the SUSY Index on the 2nd Sheet
• Central charges and RG flow of strongly-coupled N=2 theory
• Chiral algebra of Argyres-Douglas theory from M5 brane
• High-temperature asymptotics of supersymmetric partition functions
• Asymptotic growth of the 4d $\mathcal{N}=4$ index and partially deconfined phases
• $(0,4)$ dualities
• Dual Giant Gravitons in Sasaki-Einstein Backgrounds
• Holographic renormalization and supersymmetry
• Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
• Supercurrent anomalies in 4d SCFTs
• On the reduction of 4d N=1 theories on S^2
• Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions
• High-Temperature Expansion of Supersymmetric Partition Functions
• Comments on the Casimir energy in supersymmetric field theories
• Universal Asymptotics for High Energy CFT Data
• On a modular property of N=2 superconformal theories in four dimensions
• The gravity dual of supersymmetric gauge theories on a squashed $S^1\times S^3$
• The long flow to freedom
• Supersymmetric counterterms from new minimal supergravity
• Supersymmetric Renyi Entropy and Anomalies in Six-Dimensional (1,0) Superconformal Theories
• The holographic supersymmetric Casimir energy
• New 2d $\mathcal{N}=(0,2)$ dualities from four dimensions
• Schur sector of Argyres-Douglas theory and $W$-algebra
• On mass spectrum in 't Hooft's 2D model of mesons
• The character of the supersymmetric Casimir energy
• A 2d (0,2) appetizer
• EFT Asymptotics: the Growth of Operator Degeneracy
• A Meinardus theorem with multiple singularities
• Scalar Modular Bootstrap and Zeros of the Riemann Zeta Function
• Supersymmetric Casimir Energy and $\mathrm{SL}(3,\mathbb{Z})$ Transformations
• T-Reflection
• Notes on two-dimensional pure supersymmetric gauge theories
• Quantum Corrections to Central Charges and Supersymmetric Casimir Energy in AdS${}_3$/CFT${}_2$
• M2-branes and plane partitions
• Two-dimensional supersymmetric gauge theories with exceptional gauge groups
• Modified elliptic gamma functions and 6d superconformal indices
• Asymptotic degeneracies of M2-brane SCFTs
• 2d dualities from 4d

Cited by in corpus (1)

• Holographic spectral functions for Sasaki-Einstein 5-manifolds