Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills

Abstract

We perform a numerical bootstrap study of the mixed correlator system containing the half-BPS operators of dimension two and three in $\mathcal{N}=4$ Super Yang-Mills. This setup improves on previous works in the literature that only considered single correlators of one or the other operator. We obtain upper bounds on the leading twist in a given representation of the R-symmetry by imposing gaps on the twist of all operators rather than the dimension of a single one. As a result we find a tension between the large $N$ supergravity predictions and the numerical finite $N$ results already at $N\sim 100$. A few possible solutions are discussed: the extremal spectrum suggests that at large but finite $N$, in addition to the double trace operators, there exists a second tower of states with smaller dimension. We also obtain new bounds on the dimension of operators which were not accessible with a single correlator setup. Finally we consider bounds on the OPE coefficients of various operators. The results obtained for the OPE coefficient of the lightest scalar singlet show evidences of a two dimensional conformal manifold.

arXiv comment40 pages, 12 figures, 4 tables

References in corpus (46)

• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Infinite Chiral Symmetry in Four Dimensions
• The Analytic Bootstrap and AdS Superhorizon Locality
• Analyticity in Spin in Conformal Theories
• Convexity and Liberation at Large Spin
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• Carving Out the Space of 4D CFTs
• The N=4 Superconformal Bootstrap
• Bootstrapping Conformal Field Theories with the Extremal Functional Method
• Superconformal Symmetry, Correlation Functions and the Operator Product Expansion
• Large Spin Perturbation Theory
• Loops in AdS from Conformal Field Theory
• A spacetime derivation of the Lorentzian OPE inversion formula
• Superconformal Ward Identities and their Solution
• Gravitational S-matrix from CFT dispersion relations
• Carving out OPE space and precise $O(2)$ model critical exponents
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• $\mathcal{N}=4$ Super-Yang-Mills Correlators at Strong Coupling from String Theory and Localization
• Operator Product Expansion of the Lowest Weight CPOs in N=4 SYM_4 at Strong Coupling
• All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry
• Quantum Gravity from Conformal Field Theory
• Rigorous Limits on the Interaction Strength in Quantum Field Theory
• Correlation Functions and Massive Kaluza-Klein Modes in the AdS/CFT Correspondence
• The Operator Product Expansion of N=4 SYM and the 4-point Functions of Supergravity
• Unmixing Supergravity
• Analytic bootstrap at large spin
• Solving CFTs with Weakly Broken Higher Spin Symmetry
• Bounds for OPE coefficients on the Regge trajectory
• Conformal Partial Wave Expansions for N=4 Chiral Four Point Functions
• Genus-One String Amplitudes from Conformal Field Theory
• Far Beyond the Planar Limit in Strongly-Coupled $\mathcal{N}=4$ SYM
• Non-forward NLO BFKL Kernel
• Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling
• The double-trace spectrum of N=4 SYM at strong coupling
• Loop corrections for Kaluza-Klein AdS amplitudes
• Genus-2 Holographic Correlator on $Ad{S}_5\times S^5$ from Localization
• Conformal Bootstrap in the Regge Limit
• More $\mathcal{N}=4$ superconformal bootstrap
• N=4 Superconformal Characters and Partition Functions
• The M-theory Archipelago
• The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
• Conformal partial wave analysis of AdS amplitudes for dilaton-axion four-point functions
• Crossing symmetry and Higher spin towers
• Conformal Regge Theory at Finite Boost

Cited by in corpus (10)

• Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
• New Developments in the Numerical Conformal Bootstrap
• Modular invariant holographic correlators for $\mathcal{N}=4$ SYM with general gauge group
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• Bootstrapping 4d $\mathcal{N}=2$ gauge theories: the case of SQCD
• Pure anti-de Sitter supergravity and the conformal bootstrap
• OPE coefficients in Argyres-Douglas theories
• The tricritical Ising CFT and conformal bootstrap
• Bootstrapping (D, D) Conformal Matter
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories