On Superconformal Characters and Partition Functions in Three Dimensions

Abstract

Possible short and semi-short positive energy, unitary representations of the Osp(2N|4) superconformal group in three dimensions are discussed. Corresponding character formulae are obtained, consistent with character formulae for the SO(3,2) conformal group, revealing long multiplet decomposition at unitarity bounds in a simple way. Limits, corresponding to reduction to various Osp(2N|4) subalgebras, are taken in the characters that isolate contributions from fewer states, at a given unitarity threshold, leading to considerably simpler formulae. Via these limits, applied to partition functions, closed formulae for the generating functions for numbers of BPS operators in the free field limit of superconformal U(n)\times U(n) \N=6 Chern Simons theory and its supergravity dual are obtained in the large n limit. Partial counting of semi-short operators is performed and consistency between operator counting for the free field and supergravity limits with long multiplet decomposition rules is explicitly demonstrated. Partition functions counting certain protected scalar primary semi-short operators, and their superconformal descendants, are proposed and computed for large n. Certain chiral ring partition functions are discussed from a combinatorial perspective.

54 pages; uses harvmac; v.2. Table 1 and s. 4 reorganised to take more account of conserved current multiplets, conclusion rewritten slightly differently, typos corrected, references added; v.3. typos corrected, reference improved

References in corpus (21)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Comments on Multiple M2-branes
• Fractional M2-branes
• Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Seiberg Duality in Chern-Simons Theory
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• The Bethe ansatz for superconformal Chern-Simons
• The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
• The all loop AdS4/CFT3 Bethe ansatz
• Superconformal Indices for $\mathcal{N}=6$ Chern Simons Theories
• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
• Integrable Spin Chain in Superconformal Chern-Simons Theory
• AdS4/CFT3 at One Loop
• Counting BPS operators in N=4 SYM
• Comments on 1/16 BPS Quantum States and Classical Configurations
• Seiberg Duality in Chern-Simons Theories with Fundamental and Adjoint Matter
• N=4 Superconformal Characters and Partition Functions
• Conjectures for Large N Superconformal N=4 Chiral Primary Four Point Functions
• An Index for Non-relativistic Superconformal Field Theories
• Partition Functions for Membrane Theories

Cited by in corpus (33)

• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• From 4d superconformal indices to 3d partition functions
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Deformation quantization and superconformal symmetry in three dimensions
• Solving M-theory with the Conformal Bootstrap
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• The M-theory Archipelago
• Massive Anti-de Sitter Gravity from String Theory
• Studying superconformal symmetry enhancement through indices
• The star-triangle relation and 3d superconformal indices
• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• Universal Bounds on Operator Dimensions from the Average Null Energy Condition
• AdS${}_4$/CFT${}_3$ for Unprotected Operators
• On correlation functions of BPS operators in $3d$ $\mathcal{N}=6$ superconformal theories
• Supersymmetric Indices of 3d S-fold SCFTs
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• Supersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations
• Basic hypergeometry of supersymmetric dualities
• N=2 Moduli of AdS4 vacua: A fine-print study
• Precision Spectroscopy and Higher Spin symmetry in the ABJM model
• A New Duality Between $\mathcal{N}=8$ Superconformal Field Theories in Three Dimensions
• 3d N=4 Bootstrap and Mirror Symmetry
• Twisted Sectors in Gravity Duals of N=4 Chern-Simons Theories
• Marginal Deformations of 3d N=4 Linear Quiver Theories
• $\mathcal{N}=2$ Supersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations
• Duality walls in the 4d N=2 SU(N) gauge theory with 2N flavours
• Constructing Operator Basis in Supersymmetry: A Hilbert Series Approach
• Integral pentagon relations for 3d superconformal indices
• On the Kähler-Hodge structure of superconformal manifolds
• One-loop supergravity on ${\mathrm{AdS}}_4\times S^7/{\mathbb{Z}}_k$ and comparison with ABJM theory
• Masses, Sheets and Rigid SCFTs
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM