Quantum Wrapped Giant Magnon

TL;DR

The paper tackles finite-size corrections to the fundamental excitation of the AdS5 x S5 string, the giant magnon, by deriving the leading quantum exponential correction via two complementary routes: an algebraic-curve (finite-volume fluctuation) analysis and Luscher F-term calculations based on the worldsheet S-matrix. The authors obtain a concrete all-orders agreement between the curve-based computation and the F-term, providing a nontrivial cross-check of the AdS/CFT S-matrix and strengthening the control over finite-volume spectra in integrable string theories. They further interpret the fluctuation spectrum in terms of quasimomenta and log-cut structures, and discuss the potential generalizations to other string configurations, including dyons and multi-magnon states, as well as higher-loop corrections. Overall, the work lays a framework for systematically computing finite-volume corrections in this integrable setting and suggests avenues for extending these results to broader classes of string solutions.

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.

Figures (2)

• Figure 1: The two leading processes contributing to the corrections of the dispersion relation in finite volume: The F-term (LHS) describes the contribution of a virtual particle loop. We shall see that it accounts for the leading contribution or $\mathcal{O}$e^-2π Δ/√λ$$ correction to the giant magnon one-loop energy. The $\mu$-term (RHS) is the effect of a particle splitting into two on-shell particles and computes the classical finite-size effects. It also contributes to the $1$-loop shift, but since it is $\mathcal{O}$e^-2π Δ/√λp2$$, this contribution is subleading.
• Figure 2: The small charge dyonic giant magnon in finite volume Vicedo:2007rp: the endpoints of the log-cut between $X^+$ and $X^-$ develop small square root tails, separated by $\mathcal{O}$e^- π J p/2$$, which will induce finite size corrections of this order. For the classical finite-size corrections, these were the only contributions. However, as we explain in the main text, for the leading quantum corrrection there are more important corrections, which are of order $\mathcal{O}$e^-2π J$$.