Comment on strings in AdS3 × S3 × S3 × S1 at one loop

This paper studies semiclassical strings in AdS3 × S3 × S3 × S1 using the algebraic curve. Calculating one-loop corrections to the energy of the giant magnon fixes the constant term c in the expansion of the coupling h(λ). Comparing these to similar corrections for long spinning strings gives a prediction for the one-loop term f1 in the expansion of the cusp anomalous dimension f (h), for all α (where α → 1 is the AdS3 × S3 × T4 limit). For these semiclassical mode sums there is a similar choice of regularisation prescriptions to that encountered in AdS4 × CP3. However at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha \ne \frac{1}{2}$\end{document} they lead to different values of f1 and are therefore not related by a simple change of the coupling. The algebraic curve is also used to calculate various finite-size corrections for giant magnons, which are well-behaved as α → 1, and can be compared to the recently published S-matrices.