A study of integrable form factors in massless relativistic AdS_3

TL;DR

This paper investigates the massless integrable sector of AdS_3 superstring theory, deriving exact form factors and analyzing their properties, with implications for understanding integrability and potential links to the hexagon approach.

Contribution

It provides explicit formulas for minimal form factors in the massless AdS_3 setting and compares them with known Bethe ansatz methods, advancing the understanding of integrable models in string theory.

Findings

Derived exact two- and three-particle form factors

Validated formulas through complex consistency checks

Identified similarities and differences with Bethe ansatz approaches

Abstract

We show that the massless integrable sector of the AdS_3 \times S^3 \times T^4 superstring theory, which admits a non-trivial relativistic limit, provides a setting where it is possible to determine exact minimal solutions to the form factor axioms, in integral form, based on analiticity considerations, along the same lines of ordinary relativistic integrable models. We construct in full detail the formulas for the two- and three-particle case, and show the similarities as well as the differences with respect to the off-shell Bethe ansatz procedure of Babujian et al. We show that our expressions pass a series of non-trivial consistency checks which are substantially more involved than in the traditional case. We speculate on the problems concerned in a possible generalisation to an arbitrary number of particles, and on a possible connection with the hexagon programme.