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

TL;DR

This paper computes 1-loop holographic correlators in 3d ABJ(M) theory at strong coupling using Lorentzian inversion, matches them with 11d M-theory S-matrix, and confirms the results with localization and bootstrap bounds.

Contribution

It provides the first detailed 1-loop correction calculation in the holographic dual of ABJ(M) theory, including fixing contact terms via analytic continuation and localization.

Findings

Precise match between 1-loop correlator and 11d M-theory S-matrix in flat space limit.

Conjectural fixing of contact terms through analytic continuation and localization verification.

1-loop corrections saturate conformal bootstrap bounds at large N.

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 $AdS_4\times S^7/\mathbb{Z}_2$. 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.