Quantum dispersion relations for the $AdS_4 \times CP^3$ GKP string

TL;DR

This paper calculates one-loop quantum corrections to the energy-momentum relations of string excitations in the $AdS_4 imes CP^3$ background, comparing results with integrability predictions and noting some discrepancies.

Contribution

It provides the first detailed one-loop correction calculations for the GKP string in $AdS_4 imes CP^3$, extending the understanding of quantum effects in this duality.

Findings

One-loop corrections are consistent with Bethe ansatz predictions.

Results show some known discrepancies with integrability-based predictions.

The study parallels previous work in $AdS_5 imes S^5$ with new insights for $AdS_4 imes CP^3$.

Abstract

We compute the one-loop correction to the dispersion relations of the excitations of the $AdS_4 \times CP^3$ sigma model dual to ABJM theory, expanded around the cusp background. The results parallel those of N = 4 SYM. As in that case, the dispersion relations are compatible with the predictions from the Bethe ansatz for the GKP string, though showing some known discrepancies on which we comment.