Ground state energy of twisted AdS3 × S3 × T4 superstring and the TBA
Sergey Frolov, Anton Pribytok, Alessandro Sfondrini
Abstract
A bstract 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 $$ \mathcal{J} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>J</mml:mi> </mml:math> ≡ 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 /(4 L 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.