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

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Abstract

We study string corrections to one-loop amplitudes of single-particle operators ${\cal O}_p$ in $AdS_5 \times S^5$. 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 $\langle {\cal O}_{p_1}{\cal O}_{p_2}{\cal O}_{p_3} {\cal O}_{p_4}\rangle$ at order $(\alpha')^3$, 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 $AdS_5\times S^5$ 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.

Text
2207.13084v1 - Author's Original

Accepted/In Press date: 26 July 2022
Additional Information: 32 pages, extended introduction containing summary of results, 2 appendices
Keywords: hep-th

Identifiers

Local EPrints ID: 472303
URI: http://eprints.soton.ac.uk/id/eprint/472303
PURE UUID: 96579c46-7d49-4e2e-ba99-968290406d7d

Catalogue record

Date deposited: 30 Nov 2022 18:03

Contributors

Author: F. Aprile
Author: J. M. Drummond
Author: R. Glew
Author: M. Santagata