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 AdS4 × S7/ℤ2. 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 R4 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.
Highlights
That the M-theory S-matrix could be defined to all orders by first computing the dual CFT correlator at large N and taking the flat space limit
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 AdS4 × S7/Z2
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 R4 vertices, up to a finite number of contact terms that contribute to low spins where the inversion formula does not converge
Summary
We start by discussing the large cT ∼ N 3/2 expansion of four-point functions of the dimension p2 scalar bottom component of half-BPS supermultiplets in N = 8 ABJ(M) theory, and derive the data needed for the 1-loop terms for k = 2 ABJ(M) . We discuss the generalized free field theory (GFFT) that describes the cT → ∞ limit, which we use to compute average OPE coefficients of double-trace singlet long multiplets in qqpp. Afterwards, we consider tree level corrections to 22pp for even p, which we use to derive the average anomalous dimension of singlet long multiplets at orders 1/cT and 1/c5T/3 that correspond to tree level supergravity and R4, respectively. We discuss higher orders in the large cT expansion of 2222 , which will be our main focus in the rest of the paper
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