Finite-Size Effects for Multi-Magnon States

TL;DR

This paper introduces a generalized Luscher formula to accurately compute finite-size energy corrections for multi-magnon states in integrable models, validated at classical, one-loop, strong, and weak coupling levels.

Contribution

It presents a novel generalized Luscher formula for multi-magnon states, extending finite-size correction calculations across different coupling regimes.

Findings

F-term matches the exact sinh-Gordon spectrum

Mu-term aligns with Bethe Ansatz magnon boundstates

Transcendental terms emerge from BPS boundstates sum

Abstract

We propose the generalized Luscher formula for multi-magnon states by which one can compute the finite-size correction to the energy of multi giant magnons at classical and one-loop levels. It is shown that the F-term of our formula is consistent with the exact finite-size spectrum of the sinh-Gordon model, and the mu-term agrees with the finite-size energy of magnon boundstate of the asymptotic Bethe Ansatz in the su(2) sector at strong coupling. In an appendix, we evaluate our formula at weak coupling under some approximations, and find that the transcendental terms arise from a sum over an infinite tower of BPS boundstates.