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

Abstract

Abstract We study string corrections to one-loop amplitudes of single-particle operators O $$ \mathcal{O} $$ p in AdS 5 ×S 5. 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 p i=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 O p 1 O p 2 O p 3 O p 4 $$ \left\langle {\mathcal{O}}_{p1}{\mathcal{O}}_{p2}{\mathcal{O}}_{p3}{\mathcal{O}}_{p4}\right\rangle $$ at order (α′)3, valid for arbitrary external charges p i . 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 AdS 5 × S 5 amplitude, our one-loop amplitude naturally splits the S 5 part into two separate contributions. The amplitude also exhibits a remarkable consistency with the corresponding flat space IIB amplitude through the large p limit.

Keywords

• 1/N Expansion
• AdS-CFT Correspondence
• Scattering Amplitudes