Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop

TL;DR

This paper uses algebraic curve techniques to compute one-loop corrections in AdS3 x S3 x S3 x S1, fixing key parameters and predicting the cusp anomalous dimension, while analyzing finite-size effects and regularization issues.

Contribution

It provides the first detailed one-loop correction calculations for semiclassical strings in AdS3 x S3 x S3 x S1, including fixing the constant term in the coupling expansion and predicting the cusp anomalous dimension.

Findings

Calculated one-loop energy corrections for giant magnons.

Predicted the one-loop term in the cusp anomalous dimension for all lpha.

Analyzed regularization dependence and finite-size corrections.

Abstract

This paper studies semiclassical strings in AdS3 x S3 x S3 x 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(\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 AdS3 x S3 x T4 limit). For these semiclassical mode sums there is a similar choice of regularisation prescriptions to that encountered in AdS4 x CP3. However at \alpha \neq 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.