Simplicity of AdS supergravity at one loop

Abstract

A bstract We demonstrate the simplicity of AdS 5 × S 5 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 $$ \left\langle {\mathcal{O}}_2^{SG}{\mathcal{O}}_2^{SG}{\mathcal{O}}_p^{SG}{\mathcal{O}}_p^{SG}\right\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mrow> <mml:msubsup> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> <mml:mi>SG</mml:mi> </mml:msubsup> <mml:msubsup> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> <mml:mi>SG</mml:mi> </mml:msubsup> <mml:msubsup> <mml:mi>O</mml:mi> <mml:mi>p</mml:mi> <mml:mi>SG</mml:mi> </mml:msubsup> <mml:msubsup> <mml:mi>O</mml:mi> <mml:mi>p</mml:mi> <mml:mi>SG</mml:mi> </mml:msubsup> </mml:mrow> </mml:mfenced> </mml:math> 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.

Topics & Concepts