Finite-size corrections for quantum strings on AdS_4 x CP^3

TL;DR

This paper calculates finite-size curvature corrections to the energy of string states in AdS_4 x CP^3, confirming the absence of one-loop corrections to the magnon dispersion relation and identifying finite-size effects.

Contribution

It provides a detailed computation of curvature corrections at order 1/R^2 for type IIA strings on AdS_4 x CP^3, including mode cutoff prescriptions and divergence cancellations.

Findings

Logarithmic divergences cancel between Hamiltonian terms

Heavy mode cutoff is twice the light mode cutoff

No one-loop correction to the h(λ) function in the magnon dispersion

Abstract

We revisit the calculation of curvature corrections to the pp-wave energy of type IIA string states on AdS_4 x CP^3 initiated in arXiv:0807.1527. Using the near pp-wave Hamiltonian found in arXiv:0912.2257, we compute the first non-vanishing correction to the energy of a set of bosonic string states at order 1/R^2, where R is the curvature radius of the background. The leading curvature corrections give rise to cubic, order 1/R, and quartic, order 1/R^2, terms in the Hamiltonian, for which we implement the appropriate normal ordering prescription. Including the contributions from all possible fermionic and bosonic string states, we find that there exist logarithmic divergences in the sums over mode numbers which cancel between the cubic and quartic Hamiltonian. We show that the cubic Hamiltonian naturally requires that the cutoff for summing over heavy modes must be twice the one for light modes. With this prescription the strong-weak coupling interpolating function h(\lambda), entering the magnon dispersion relation, does not receive a one-loop correction, in agreement with the algebraic curve spectrum. However, the single magnon dispersion relation exhibits finite-size exponential corrections.