Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills

TL;DR

This paper investigates the structure of Reggeon bound states in strongly-coupled $ ext{N}=4$ super Yang-Mills theory, revealing constraints on excitations in the multi-Regge limit and relating BFKL eigenvalues across different particle numbers.

Contribution

It demonstrates that the excitations in the multi-Regge limit are highly constrained and that Reggeon bound state eigenvalues are multiples of the six-gluon case, extending understanding of scattering amplitudes.

Findings

BFKL eigenvalues of Reggeon bound states are multiples of the six-gluon case eigenvalue.

The set of excitations in the multi-Regge limit is highly constrained.

Analytic continuations for any number of particles follow similar excitation patterns.

Abstract

The multi-Regge limit of scattering amplitudes in strongly-coupled $\mathcal{N}=4$ super Yang-Mills is described by the large mass limit of a set of thermodynamic Bethe ansatz (TBA) equations. A non-trivial remainder function arises in this setup in certain kinematical regions due to excitations of the TBA equations which appear during the analytic continuation into these kinematical regions. So far, these analytic continuations were carried out on a case-by-case basis for the six- and seven-gluon remainder function. In this note, we show that the set of possible excitations appearing in any analytic continuation in the multi-Regge limit for any number of particles is rather constrained. In particular, we show that the BFKL eigenvalue of any possible Reggeon bound state is a multiple of the two-Reggeon BFKL eigenvalue appearing in the six-gluon case.