Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz

TL;DR

This paper computes finite size corrections to the spectrum of strings in AdS_4 x CP^3, showing precise agreement with Bethe Ansatz predictions and analyzing the spectrum of magnon states.

Contribution

It provides the first curvature correction calculations in AdS_4 x CP^3 string theory and demonstrates their exact match with all-loop Bethe Ansatz results.

Findings

Finite size spectrum corrections match Bethe Ansatz predictions.

One-loop dispersion relations are finite and free of ambiguities.

Spectrum of two-magnon states is fully determined and agrees with Bethe Ansatz.

Abstract

We compute the first curvature corrections to the spectrum of light-cone gauge type IIA string theory that arise in the expansion of $AdS_4\times \mathbb{CP}^3$ about a plane-wave limit. The resulting spectrum is shown to match precisely, both in magnitude and degeneration that of the corresponding solutions of the all-loop Gromov--Vieira Bethe Ansatz. The one-loop dispersion relation correction is calculated for all the single oscillator states of the theory, with the level matching condition lifted. It is shown to have all logarithmic divergences cancelled and to leave only a finite exponentially suppressed contribution, as shown earlier for light bosons. We argue that there is no ambiguity in the choice of the regularization for the self-energy sum, since the regularization applied is the only one preserving unitarity. Interaction matrices in the full degenerate two-oscillator sector are calculated and the spectrum of all two light magnon oscillators is completely determined. The same finite-size corrections, at the order 1/J, where $J$ is the length of the chain, in the two-magnon sector are calculated from the all loop Bethe Ansatz. The corrections obtained by the two completely different methods coincide up to the fourth order in $\lambda' =\lambda/J^2$. We conjecture that the equivalence extends to all orders in $\lambda$ and to higher orders in 1/J.