Abstract
We demonstrate the simplicity of AdS5× S5 IIB supergravity at one loop level, by studying non-planar holographic four-point correlators in Mellin space. We develop a systematic algorithm for constructing one-loop Mellin amplitudes from the tree-level data, and obtain a simple closed form answer for the leftlangle {mathcal{O}}_2^{SG}{mathcal{O}}_2^{SG}{mathcal{O}}_p^{SG}{mathcal{O}}_p^{SG}rightrangle correlators. The structure of this expression is remarkably simple, containing only simultaneous poles in the Mellin variables. We also study the flat space limit of the Mellin amplitudes, which reproduces precisely the IIB supergravity one-loop amplitude in ten dimensions. Our results provide nontrivial evidence for the persistence of the hidden conformal symmetry at one loop.
Highlights
While the program of AdS scattering amplitudes was initiated a long time ago, only recently have truly efficient computational methods been developed
We demonstrate the simplicity of AdS5 × S5 IIB supergravity at one loop level, by studying non-planar holographic four-point correlators in Mellin space
We develop a systematic algorithm for constructing one-loop Mellin amplitudes from the tree-level data, and obtain a simple closed form answer for the O2SGO2SGOpSGOpSG correlators
Summary
One-half BPS operators are super primaries of short representations of the superconformal group PSU(2, 2|4). Let us first recall that supergravity fields from the Kaluza-Klein reduction are not mapped to single-trace operators under the duality dictionary [12, 41, 48, 49] This is best illustrated by considering a simple example of a three-point function, namely. For any {qi} satisfying the above partition conditions These single-particle operators are identified with the Kaluza-Klein reduction of the supergravity fields. We can establish a relation between the supergravity states of IIB supergravity on AdS3 × S3 × K3 (or T 4), and the one-half BPS operators at the orbifold point In the latter case operators are more naturally graded by the number of twist operators inserted, which is similar to the trace number in the N = 4 SYM case. The objective of this section is to review the superconformal kinematics of these correlators
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