Ground state energy of twisted AdS 3 × S 3 × T 4 superstring and the TBA
Sergey Frolov (Hamilton Mathematics Institute and School of Mathematics, Trinity College, Dublin 2, Ireland); Anton Pribytok (Institut für Physik, Humboldt-Universität zu Berlin, Zum Großen Windkanal 2, Berlin, 12489, Germany); Alessandro Sfondrini (Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via Marzolo 8, Padova, 35131, Italy, Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, via Marzolo 8, Padova, 35131, Italy, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey, 08540, USA)
We use the lightcone AdS 3 × S 3 × T 4 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 $$ \mathcal{J} $$ ≡ L/h is kept fixed. We then analyse the ground state energy of the model by means of the mirror TBA equations for the AdS 3 × S 3 × T 4 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 T 4 bosons and fermions can be computed exactly, and is shown to be proportional to hL/(4L 2 – 1). Comparison with the semi-classical result shows that the TBA equations involve only one Y 0-function for massless excitations but not two as was conjectured before. Some of the results obtained are generalised to the mixed-flux AdS 3 × S 3 × T 4 superstring.
