ABJ Correlators with Weakly Broken Higher Spin Symmetry

Abstract

We consider four-point functions of operators in the stress tensor multiplet of the 3d $\mathcal{N}=6$ $U(N{)}_k\times U(N+M{)}_{-k}$ or $SO(2{)}_{2k}\times USp(2+2M{)}_{-k}$ ABJ theories in the limit where $M$ and $k$ are taken to infinity while $N$ and $\lambda \sim M/k$ are held fixed. In this limit, these theories have weakly broken higher spin symmetry and are holographically dual to $\mathcal{N}=6$ higher spin gravity on $Ad{S}_4$, where $\lambda$ is dual to the bulk parity breaking parameter. We use the weakly broken higher spin Ward identities, superconformal Ward identities, and the Lorentzian inversion formula to fully determine the tree level stress tensor multiplet four-point function up to two free parameters. We then use supersymmetric localization to fix both parameters for the ABJ theories in terms of $\lambda$, so that our result for the tree level correlator interpolates between the free theory at $\lambda =0$ and a parity invariant interacting theory at $\lambda =1/2$. We compare the CFT data extracted from this correlator to a recent numerical bootstrap conjecture for the exact spectrum of $U(1{)}_{2M}\times U(1+M{)}_{-2M}$ ABJ theory (i.e. $\lambda =1/2$ and $N=1$), and find good agreement in the higher spin regime.

arXiv comment48 pages plus appendices, 2 figures

References in corpus (47)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• AdS Dual of the Critical O(N) Vector Model
• Bounding scalar operator dimensions in 4D CFT
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Conformal Four Point Functions and the Operator Product Expansion
• Fractional M2-branes
• Conformal Partial Waves and the Operator Product Expansion
• Writing CFT correlation functions as AdS scattering amplitudes
• SUSY Gauge Theories on Squashed Three-Spheres
• Analyticity in Spin in Conformal Theories
• Notes on SUSY Gauge Theories on Three-Sphere
• Higher-Spin Gauge Theories in Four, Three and Two Dimensions
• Projectors, Shadows, and Conformal Blocks
• Bootstrapping the O(N) Vector Models
• How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples
• The N=4 Superconformal Bootstrap
• Constraining conformal field theories with a slightly broken higher spin symmetry
• Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories
• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• The $(2,0)$ superconformal bootstrap
• Loops in AdS from Conformal Field Theory
• How to Succeed at Holographic Correlators Without Really Trying
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Higher-Spin Gauge Theories and Bulk Locality
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• Deformation quantization and superconformal symmetry in three dimensions
• ABJ Triality: from Higher Spin Fields to Strings
• More Holography from Conformal Field Theory
• More $\mathcal{N}=4$ superconformal bootstrap
• Solving M-theory with the Conformal Bootstrap
• The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity
• On Superconformal Four-Point Mellin Amplitudes in Dimension $d>2$
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• A Derivation of AdS/CFT for Vector Models
• The M-theory Archipelago
• Veneziano Amplitude of Vasiliev Theory
• The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories
• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• 6d (2,0) and M-theory at 1-loop
• AdS${}_4$/CFT${}_3$ for Unprotected Operators
• Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
• Four-point functions in large $N$ Chern-Simons fermionic theories
• ABJ Quadrality
• ABJ Theory in the Higher Spin Limit

Cited by in corpus (7)

• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• Modular invariant holographic correlators for $\mathcal{N}=4$ SYM with general gauge group
• Pure anti-de Sitter supergravity and the conformal bootstrap
• Holographic S-fold theories at one loop
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• AdS from CFT for scalar QED
• The Holographic Contributions to the Sphere Free Energy