ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion

Abstract

We study the stress tensor multiplet four-point function in the 3d maximally supersymmetric ABJ(M) theory with Chern-Simons level $k=2$, which in the large $N$ limit is holographically dual to weakly coupled M-theory on $Ad{S}_4\times S^7/{\mathbb{Z}}_2$. We use the Lorentzian inversion to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity $R$ and the first higher derivative correction $R^4$ vertices, up to a finite number of contact terms that contribute to low spins where the inversion formula does not converge. We find a precise match with the corresponding terms in the 11d M-theory S-matrix by taking the flat space limit, which is not sensitive to these contact terms. We then conjecturally fix these contact terms by analytically continuing the inversion formula below its expected range of convergence, and verify this conjecture using supersymmetric localization. Finally, we compare some of the 1-loop CFT data to non-perturbative in $N$ bounds from the numerical conformal bootstrap, which we compute at unprecedently high accuracy, and find that the 1-loop corrections saturate the bounds in the large $N$ regime, which extends the previously observed match at tree level.

47 pages + appendices, 3 figures. v3 typos corrected, accepted to JHEP

References in corpus (11)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Holography from Conformal Field Theory
• Fractional M2-branes
• Writing CFT correlation functions as AdS scattering amplitudes
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling
• Squashing, Mass, and Holography for 3d Sphere Free Energy
• ABJ Correlators with Weakly Broken Higher Spin Symmetry
• Four point functions in CFT's with slightly broken higher spin symmetry
• Regge trajectories for the (2,0) theories

Cited by in corpus (12)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• One-loop Gluon Amplitudes in AdS
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• Higher Derivative Supergravities in Diverse Dimensions
• Comments on ABJM free energy on $S^3$ at large $N$ and perturbative expansions in M-theory and string theory
• Lattice studies of supersymmetric gauge theories
• Pure anti-de Sitter supergravity and the conformal bootstrap
• Conformal bounds in three dimensions from entanglement entropy
• Holographic S-fold theories at one loop
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
• The Holographic Contributions to the Sphere Free Energy