Character Formulae and Partition Functions in Higher Dimensional Conformal Field Theory

Abstract

A discussion of character formulae for positive energy unitary irreducible representations of the the conformal group is given, employing Verma modules and Weyl group reflections. Product formulae for various conformal group representations are found. These include generalisations of those found by Flato and Fronsdal for SO(3,2). In even dimensions the products for free representations split into two types depending on whether the dimension is divisible by four or not.

43 pages, uses harvmac,version 2 2 references added, minor typos corrected

Cited by in corpus (75)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• W Symmetry in six dimensions
• Operator bases, $S$-matrices, and their partition functions
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• BMS Particles in Three Dimensions
• Geometric Formulation for Partially Massless Fields
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d
• Counting BPS operators in N=4 SYM
• Higher-spin algebras and cubic interactions for simple mixed-symmetry fields in AdS spacetime
• Mixed-symmetry fields in de Sitter space: a group theoretical glance
• Partition function of free conformal higher spin theory
• The critical O(N) CFT: Methods and conformal data
• Effective Field Theory of Gravity to All Orders
• N=4 Superconformal Characters and Partition Functions
• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
• Free box^k Scalar Conformal Field Theory
• Dimensional Reduction for Conformal Blocks
• Spinning operators and defects in conformal field theory
• Exceptional F(4) Higher-Spin Theory in AdS(6) at One-Loop and other Tests of Duality
• Aspects of Superconformal Multiplets in D>4
• On Superconformal Characters and Partition Functions in Three Dimensions
• TASI Lectures on the Higher Spin - CFT duality
• Partition Functions for Higher-Spin theories in AdS
• Flato-Fronsdal theorem for higher-order singletons
• Partition Functions, the Bekenstein Bound and Temperature Inversion in Anti-de Sitter Space and its Conformal Boundary
• Revisiting the dilatation operator of the Wilson-Fisher fixed point
• Anomalies and the Helicity of the Thermal State
• Thermal Conformal Blocks
• A note on the representations of $\text{SO}(1,d+1)$
• Rotating Higher Spin Partition Functions and Extended BMS Symmetries
• 2, 84, 30, 993, 560, 15456, 11962, 261485, ...: Higher dimension operators in the SM EFT
• Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT
• One-loop Test of Free SU(N) Adjoint Model Holography
• Characters and Group Invariant Polynomials of (Super)fields: Road to "Lagrangian"
• Hilbert Series and Plethystics: Paving the path towards 2HDM- and MLRSM-EFT
• AdS one-loop partition functions from bulk and edge characters
• On the Holography of Free Yang-Mills
• EFT Asymptotics: the Growth of Operator Degeneracy
• Towards higher-spin AdS${}_2$/CFT${}_1$ holography
• Higher spin de Sitter quasinormal modes
• Black Hole Scattering and Partition Functions
• Iterating free-field AdS/CFT: higher spin partition function relations
• Hints of unitarity at large $N$ in the $O(N{)}^3$ tensor field theory
• Singletons and their maximal symmetry algebras
• Free field primaries in general dimensions: Counting and construction with rings and modules
• Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra
• CFT4 as SO(4,2)-invariant TFT2
• Invariant Differential Operators and Characters of the AdS_4 Algebra
• A Note on Vectorial AdS${}_5$/CFT${}_4$ Duality for Spin-$j$ Boundary Theory
• On Singleton Composites in Non-compact WZW Models
• Constructing Operator Basis in Supersymmetry: A Hilbert Series Approach
• Evidence for 3d bosonization from monopole operators
• The Conformal Characters
• The tricritical Ising CFT and conformal bootstrap
• Constructing the bulk at the critical point of three-dimensional large $N$ vector theories
• One-Loop Free Energy of Tensionless Type IIB String in AdS${}_5\times$S${}^5$
• CFT(4) Partition Functions and the Heat Kernel on AdS(5)
• Character Integral Representation of Zeta function in AdS${}_{d+1}$: II. Application to partially-massless higher-spin gravities
• Twisted Flato-Fronsdal Theorem for Higher-Spin Algebras
• Character Integral Representation of Zeta function in AdS${}_{d+1}$: I. Derivation of the general formula
• Conformal quantum field theory in various dimensions
• Anomalous Dimensions from Thermal AdS Partition Functions
• Conformal gravity 1-loop partition function
• Anomalous Dimensions in Hypercubic Theories
• From Spinning Primaries to Permutation Orbifolds
• Interactions as conformal intertwiners in 4D QFT
• Holomorphic primary fields in free CFT4 and Calabi-Yau orbifolds
• $\mathcal{N}=4$ SYM, (super)-polynomial rings and emergent quantum mechanical symmetries
• Conformal a-anomaly of some non-unitary 6d superconformal theories
• Explicit Character Formulae for Positive Energy UIRs of D=4 Conformal Supersymmetry
• Exploring Free Matrix CFT Holographies at One-Loop