Comment on strings in AdS 3 × S 3 × S 3 × S 1 at one loop

Abstract

This paper studies semiclassical strings in AdS 3 × S 3 × S 3 × 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(λ). 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 α (where α → 1 is the AdS 3 × S 3 × T 4 limit). For these semiclassical mode sums there is a similar choice of regularisation prescriptions to that encountered in AdS 4 × CP 3. However at $\alpha \ne \frac{1}{2}$ 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 α → 1, and can be compared to the recently published S-matrices.