Giant magnons in AdS_4/CFT_3: dispersion, quantization and finite--size corrections

TL;DR

This paper analyzes giant magnon solutions in AdS4/CFT3, calculating quantum and finite-size corrections to their dispersion relation, revealing insights into the interpolating function and providing tests for the proposed S-matrix.

Contribution

It provides the first quantum correction calculations for giant magnons in AdS4/CFT3 and examines finite-size effects, offering new tests for the integrability-based S-matrix.

Findings

One-loop correction vanishes in infinite volume.

The interpolating function h(λ) lacks a constant term at strong coupling.

Finite volume corrections are computed and can test the S-matrix.

Abstract

We study giant magnon solutions in AdS4 \times CP3. We compute quantum corrections to their dispersion relation. We find out that the one--loop correction vanishes in infinite volume. This implies that the interpolating function h(\lambda) between strong and weak coupling regimes does not have a constant term \lambda^0 at strong coupling. We also compute first nonvanishing finite volume correction to the one--loop expression. When compared to the L\"{u}sher formula, our results could provide a nontrivial check of the AdS4 \times CP3 S--matrix proposed recently in arXiv:0807.1924.