Semiclassical Quantization of the Giant Magnon

TL;DR

The paper delivers a complete semiclassical quantization of the giant magnon by deriving explicit bosonic and fermionic fluctuation spectra around the classical soliton in AdS5×S5. It employs a mode-based approach, aided by the dressing method for bosons and a direct κ-symmetry–guided treatment for fermions, to compute the 1-loop functional determinant and verify that the leading quantum correction to the giant magnon energy Δ−J vanishes. The results align with supersymmetry expectations and underscore the role of stability angles in curved-string backgrounds. Overall, the work provides a detailed, checkable framework for quantum corrections to worldsheet solitons relevant to AdS/CFT and the worldsheet S-matrix.

Abstract

Solitons in field theory provide a window into regimes not directly accessible by the fundamental perturbative degrees of freedom. Motivated by interest in the worldsheet S-matrix of string theory in AdS_5 x S^5 in the limit of infinite worldsheet volume we consider the semiclassical quantization of a particular soliton of this theory: the Hofman-Maldacena `giant magnon' spinning string. We obtain explicit formulas for the complete spectrum of bosonic and fermionic fluctuations around the giant magnon. As an application of these results we confirm that the one-loop correction to the classical energy vanishes as expected.