Two-loop supergravity on AdS$_5\times$S$^5$ from CFT

Abstract

We describe a construction of the two-loop amplitude of four graviton supermultiplets in AdS 5 ×S 5 . We start from an ansatz for a preamplitude from which we generate the full amplitude under the action of a specific Casimir operator. The ansatz captures a recent ansatz of Huang and Yuan and we confirm their result through similar constraints. We identify a class of four-dimensional 'zigzag' integrals which are perfectly adapted to describing the leading logarithmic discontinuity to all orders. We also observe that a bonus crossing symmetry of the preamplitude follows from the transformation properties of the Casimir operator. Combined with the zigzag integrals this allows us to construct a crossing symmetric function with the correct leading logarithmic discontinuities in all channels.From the two-loop result we extract an explicit expression for the two-loop correction to the anomalous dimensions of twist-four operators of generic spin which includes dependence on (alternating) nested harmonic sums up to weight three. We also revisit the prescription of the bulk-point limit of AdS amplitudes and show how it recovers the full flat-space amplitude, not just its discontinuity. With this extended notion of the bulk-point limit we reproduce the scale-dependent logarithmic threshold terms of type IIB string theory in flat-space.

Scattering bound states in AdS

“…JHEP08(2022)107 polylogarithms while in the single-particle case at most dilogarithms appear. Curiously, these higher order polylogarithms also show up in loop-level correlators of single-particle operators [11,[24][25][26][27][28][29]. This seems to imply that certain tree-level diagrams with external bound states might share structural similarity with AdS loop diagrams.…”

Scattering bound states in AdS

“…Interestingly, [15] found that for n ≥ 2 the correlators necessarily contain higher order polylogarithms while in the single-particle case at most dilogarithms appear. Curiously, these higher order polylogarithms also show up in loop-level correlators of singleparticle operators [11,[21][22][23][24][25][26]. This seems to imply that certain tree-level diagrams with external bound states might share structural similarity with AdS loop diagrams.…”