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

One-loop string amplitudes in AdS5 X S5: Mellin space and sphere splitting
One-loop string amplitudes in AdS5 X S5: Mellin space and sphere splitting
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.
hep-th
Aprile, F.
09a3f224-2049-469f-87fd-fce381efb272
Drummond, J. M.
3ea15544-457f-4e72-8ad0-60f3136841db
Glew, R.
25632196-3a00-4eda-8d0a-cda513af2eb0
Santagata, M.
f4f33efa-a3bf-49cc-baa2-09660b556261
Aprile, F.
09a3f224-2049-469f-87fd-fce381efb272
Drummond, J. M.
3ea15544-457f-4e72-8ad0-60f3136841db
Glew, R.
25632196-3a00-4eda-8d0a-cda513af2eb0
Santagata, M.
f4f33efa-a3bf-49cc-baa2-09660b556261

[Unknown type: UNSPECIFIED]

Record type: UNSPECIFIED

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.

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2207.13084v1 - Author's Original
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Accepted/In Press date: 26 July 2022
Additional Information: 32 pages, extended introduction containing summary of results, 2 appendices
Keywords: hep-th

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

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Date deposited: 30 Nov 2022 18:03
Last modified: 30 Nov 2022 18:04

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Contributors

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

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