Finite size effects for giant magnons on physical strings

TL;DR

This paper derives leading order finite size energy corrections for multiple giant magnons on physical strings using finite gap methods, applicable to both fundamental and dyonic magnons, with results independent of magnon flavors.

Contribution

It provides a unified approach to compute finite size corrections for multiple giant magnons, including dyonic cases, using finite gap methods and Bethe ansatz techniques.

Findings

Energy corrections are simple and flavor-independent at leading order.

Results are valid for both fundamental and dyonic giant magnons.

Finite size effects can be systematically computed for multiple magnons.

Abstract

Using finite gap methods, we find the leading order finite size corrections for an arbitrary number of giant magnons on physical strings, where the sum of the momenta is a multiple of 2\pi. Our results are valid for the Hofman-Maldacena fundamental giant magnons as well as their dyonic generalizations. The energy corrections turn out to be surprisingly simple, especially if all the magnons are fundamental, and at leading order are independent of the magnon flavors. We also show how to use the Bethe ansatz to find finite size corrections for dyonic giant magnons with large R-charges.