One-loop string amplitudes in AdS5×S5: Mellin space and sphere splitting

Abstract

We study string corrections to one-loop amplitudes of single-particle operators mathcal{O} p in AdS5×S5. The tree-level correlators in supergravity enjoy an accidental 10d conformal symmetry. Consequently, one observes a partial degeneracy in the spectrum of anomalous dimensions of double-trace operators and at the same time equality of many different correlators for different external charges pi=1,2,3,4. The one-loop contribution is expected to lift such bonus properties, and its precise form can be predicted from tree-level data and consistency with the operator product expansion.Here we present a closed-form Mellin space formula for leftlangle {mathcal{O}}_{p1}{mathcal{O}}_{p2}{mathcal{O}}_{p3}{mathcal{O}}_{p4}rightrangle at order (α′)3, valid for arbitrary external charges pi. Our formula makes explicit the lifting of the bonus degeneracy among different correlators through a feature we refer to as ‘sphere splitting’. While tree-level Mellin amplitudes come with a single crossing symmetric kernel, which defines the pole structure of the AdS5× S5 amplitude, our one-loop amplitude naturally splits the S5 part into two separate contributions. The amplitude also exhibits a remarkable consistency with the corresponding flat space IIB amplitude through the large p limit.