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 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.

One-loop gluon amplitudes in AdS

“…• It would also be interesting to extend the one-loop analysis to other backgrounds which have AdS factors other than AdS 5 , and to explore the structure of one-loop amplitudes across different spacetime dimensions. Similar supergravity one-loop fourpoint amplitudes have been computed for eleven dimensional supergravity on AdS 7 × S 4 [20] and AdS 4 × S 7 [23].…”

“…been obtained in a variety of supergravity theories, both at tree level [1][2][3][4][5][6][7][8][9][10][11][12] and at loop level [13][14][15][16][17][18][19][20][21][22][23]. The results exhibit a remarkable simplicity which is obscured by the diagrammatic expansion and is reminiscent of the situation in flat space.…”

Bootstrapping $\mathcal{N}=4$ super-Yang-Mills on the conformal manifold

“…This would allow us to compute small precise islands for each N, M, k, as was already done for the N = 8 case with k, M = 1, 2 in [68]. For the N = 8 case itself, adding this integrated constraint as well as another possible constraint coming from the squashed sphere free energy [69,70] could make the islands so precise that we could read off large N corrections to the correlator, as initiated in [71,72], which would allow us to derive the M-theory S-matrix following [73]. We have truly only begun to explore the power of combining the conformal bootstrap with supersymmetric localization.…”

Holographic S-fold theories at one loop

“…To deal with this mixing problem, [61][62][63] proposed a general algorithm and used it to analyze N = 4 SYM. After further loop-level studies of N = 4 SYM [64][65][66][67][68], the AdS unitarity method was first applied to other fullfledged theories in [44,69,70]. 5 Before extending this list, it is important to mention [73] which represents the current state of the art for N = 4 SYM with gauge groups other than SU(N).…”