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

This paper studies semiclassical strings in AdS(3) x S-3 x S-3 x S-1 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(lambda). Comparing these to similar corrections for long spinning strings gives a prediction for the one-loop term f(1) in the expansion of the cusp anomalous dimension f(h), for all alpha (where alpha -> 1 is the AdS(3) x S-3 x T-4 limit). For these semiclassical mode sums there is a similar choice of regularisation prescriptions to that encountered in AdS(4) x CP3. However at alpha not equal 1/2 they lead to different values of f(1) 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 alpha -> 1, and can be compared to the recently published S-matrices.