Ground state energy of twisted AdS3 × S3 × T4 superstring and the TBA

We use the lightcone AdS3 × S3 × T4 superstring sigma model with fermions and bosons subject to twisted boundary conditions to find the ground state energy in the semi-classical approximation where effective string tension h and the light-cone momentum L are sent to infinity in such a way that J ≡ L/h is kept fixed. We then analyse the ground state energy of the model by means of the mirror TBA equations for the AdS3 × S3 × T4 superstring in the pure RR background. The calculation is performed for small twist μ with L and h fixed, for large L with μ and h fixed, and for small h with μ and L fixed. In these limits the contribution of the gapless worldsheet modes coming from the T4 bosons and fermions can be computed exactly, and is shown to be proportional to hL/(4L2 – 1). Comparison with the semi-classical result shows that the TBA equations involve only one Y0-function for massless excitations but not two as was conjectured before. Some of the results obtained are generalised to the mixed-flux AdS3 × S3 × T4 superstring.