Ground state energy of twisted $AdS_{3}\times S^{3}\times T^{4}$ superstring and the TBA

TL;DR

This paper calculates the ground state energy of the twisted $AdS_{3}\times S^{3}\times T^{4}$ superstring using semi-classical methods and TBA equations, revealing insights into massless modes and extending to mixed-flux backgrounds.

Contribution

It introduces a novel analysis of the ground state energy using mirror TBA equations for the twisted superstring, clarifying the role of massless modes and simplifying the TBA structure.

Findings

Ground state energy computed in various limits matches semi-classical results.

TBA equations involve only one $Y_0$-function for massless excitations.

Results extended to the mixed-flux $AdS_{3}\times S^{3}\times T^{4}$ superstring.

Abstract

We use the lightcone $AdS_{3}\times S^{3}\times T^{4}$ 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 ${\cal J}\equiv L/h$ is kept fixed. We then analyse the ground state energy of the model by means of the mirror TBA equations for the $AdS_{3}\times S^{3}\times T^{4}$ superstring in the pure RR background. The calculation is performed for small twist $\mu$ with $L$ and $h$ fixed, for large $L$ with $\mu$ and $h$ fixed, and for small $h$ with $\mu$ 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 $AdS_{3}\times S^{3}\times T^{4}$ superstring.