A new derivation of Luscher F-term and fluctuations around the giant magnon

TL;DR

This paper presents a novel derivation of the Luscher F-term formula using quadratic fluctuations, applicable to various dispersion relations, and applies it to compute finite size corrections for giant magnons.

Contribution

It introduces a general derivation of the Luscher F-term formula from quadratic fluctuations, extending its applicability to arbitrary dispersion relations.

Findings

Derived a general Luscher F-term formula from quadratic fluctuations

Computed finite size corrections for giant magnon dispersion relation

Validated the formalism for diagonal S-matrix and arbitrary dispersion relations

Abstract

In this paper we give a new derivation of the generalized Luscher F-term formula from a summation over quadratic fluctuations around a given soliton. The result is very general providing that S-matrix is diagonal and is valid for arbitrary dispersion relation. We then apply this formalism to compute the leading finite size corrections to the giant magnon dispersion relation coming from quantum fluctuations.