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

Abstract

The multi-Regge limit of scattering amplitudes in strongly-coupled $$ \mathcal{N} $$ 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.

TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling

“…Some hints on this directions can be found in [25,35,36,37]. It would be interesting to see what happens in various limits of the TBA equations in the AdS 5 case [38,39,40], which may shed light on developing the method for the finite coupling. We hope to address this question in a future publication.…”

The SAGEX review on scattering amplitudes Chapter 15: The multi-Regge limit

“…The minimal area problem is integrable and can be solved using a thermodynamic Bethe ansatz or Y-system [107][108][109]. These systems have been solved in multi-Regge limits [110][111][112][113][114][115][116], shedding light on the strong-coupling behavior, which at six-points must be consistent with the strong coupling limit of the all-orders results [55].…”