Abstract

We compute the one-loop S-matrix for the light bosonic excitations of the GKP string at strong coupling. These correspond, on the gauge theory side, to gluon insertions in the GKP vacuum. We perform the calculation by Feynman diagrams in the worldsheet theory and we compare the result to the integrability prediction, finding perfect agreement for the scheme independent part. For scheme dependent rational terms we test different schemes and find that a recent proposal reproduces exactly the integrability prediction.

Highlights

  • A paramount advance in the study of scattering amplitudes of planar N = 4 SYM has been fostered by insights from the AdS/CFT correspondence [1] and integrability [2, 3]

  • A set of axioms determines such amplitudes and in particular relates them to the scattering elements of the flux-tube theory. The latter can be identified as an operator of large spin [13] amenable of an integrable spin chain interpretation, or, at strong coupling, as the dual excited GKP string

  • For gauge excitations of the opposite helicity and backward kinematics we observe that the term proportional to π surviving the Feynman diagrams (8.10) is exactly cancelled against the opposite contribution (10.3) coming from the corrections to the tree-level amplitude induced by the dispersion relation of the gluons

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Summary

Introduction

A set of axioms determines such amplitudes and in particular relates them to the scattering elements of the flux-tube theory The latter can be identified as an operator of large spin [13] amenable of an integrable spin chain interpretation, or, at strong coupling, as the dual excited GKP string. Integrability of the flux-tube theory, the GKP string model [38, 39], allows to determine the S-matrix from a set of Bethe equations Performing their expansion at strong coupling is non-trivial. In this paper we focus on scattering between gauge excitations and compute their amplitude at next-to-leading order at strong coupling via perturbation theory in the worldsheet model. We provide several technical details in a series of appendices

Summary of the results
Lagrangian and Feynman rules
Tree-level amplitudes
Reduction to lower order topologies
Tensor reduction
Diagrams
Expression in terms of bubble integrals
Comments on the result
One-loop opposite helicity forward scattering
One-loop opposite helicity backward scattering
External legs corrections
10 Corrections to the gluon dispersion relation
11 Final results
12 Conclusions
A ABA results
B Details on the one-loop computation
C Expanded Lagrangian
Full Text
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