Diagonal Form Factors in Landau-Lifshitz Models

TL;DR

This paper computes all-order perturbative diagonal form factors in the non-relativistic Landau-Lifshitz model, resums series for low particle numbers, and applies these results to study deformations and gauge theory structure constants.

Contribution

It provides a novel all-orders perturbative computation and resummation of form factors in the Landau-Lifshitz model, extending understanding of integrable deformations.

Findings

All-order quantum form factors for low particle numbers are obtained.

Form factors are used to analyze deformations of the integrable theory.

Spin-chain S-matrix elements are computed for Leigh-Strassler deformations.

Abstract

We perturbatively study form factors in the Landau-Lifshitz model and the generalisation originating in the study of the N=4 super-Yang-Mills dilatation generator. In particular we study diagonal form factors which have previously been related to gauge theory structure constants. For the Landau-Lifshitz model, due to the non-relativistic nature of the theory, we are able to compute all orders in perturbation theory and to resum the series to find quantum form factors for low numbers of external particles. We apply our form factors to the study of deformations of the integrable theory by means of form factor perturbation theory. As a check of our method we compute spin-chain S-matrix elements for the Leigh-Strassler family of marginal deformations to leading order in the deformation parameters.