Loop corrections for Kaluza-Klein AdS amplitudes

TL;DR

This paper extends previous one-loop amplitude calculations in AdS_5 x S^5 to include Kaluza-Klein modes, providing explicit formulas for anomalous dimensions of double-trace operators, advancing understanding of quantum corrections in holographic duals.

Contribution

It introduces a method to compute one-loop amplitudes involving Kaluza-Klein modes in AdS_5 x S^5, including explicit anomalous dimension formulas for twist five operators.

Findings

Derived one-loop amplitudes with KK modes in AdS_5 x S^5.

Explicit formulas for anomalous dimensions of twist five double-trace operators.

Resolved large N degeneracy among long double-trace operators.

Abstract

Recently we conjectured the four-point amplitude of graviton multiplets in ${\rm AdS}_5 \times {\rm S}^5$ at one loop by exploiting the operator product expansion of $\mathcal{N}=4$ super Yang-Mills theory. Here we give the first extension of those results to include Kaluza-Klein modes, obtaining the amplitude for two graviton multiplets and two states of the first KK mode. Our method again relies on resolving the large N degeneracy among a family of long double-trace operators, for which we obtain explicit formulas for the leading anomalous dimensions. Having constructed the one-loop amplitude we are able to obtain a formula for the one-loop corrections to the anomalous dimensions of all twist five double-trace operators.