Quantum Wrapped Giant Magnon

TL;DR

This paper calculates the leading finite-size exponential correction to the energy of the giant magnon in AdS5 x S5 using algebraic curve and Luscher formulas, confirming their agreement and testing the S-matrix.

Contribution

It provides the first explicit computation of finite-size corrections to the giant magnon energy using two independent methods, validating the S-matrix approach.

Findings

Agreement between algebraic curve and Luscher formula methods

Confirmation of the S-matrix's validity for finite-size corrections

Potential for extending methods to other string configurations

Abstract

Understanding the finite-size corrections to the fundamental excitations of a theory is the first step towards completely solving for the spectrum in finite volume. We compute the leading exponential correction to the quantum energy of the fundamental excitation of the light-cone gauged string in AdS(5) x S(5), which is the giant magnon solution. We present two independent ways to obtain this correction: the first approach makes use of the algebraic curve description of the giant magnon. The second relies on the purely field-theoretical Luscher formulas, which depend on the world-sheet S-matrix. We demonstrate the agreement to all orders in g/Delta of these approaches, which in particular presents a further test of the S-matrix. We comment on generalizations of this method of computation to other string configurations.