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 α 6 = 12 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. 1