$T \bar{T},J \bar T$, $T \bar{J}$ Partition Sums From String Theory

Understand

We calculate the torus partition sum of a general $CFT_2$ with left and right moving conserved currents $J$ and $\bar J$, perturbed by a combination of the irrelevant operators $T\bar T$, $J\bar T$ and $T\bar J$.

• We use string theory techniques to write it as an integral transform of the partition sum of the unperturbed CFT with chemical potentials for the left and right moving conserved charges.
• The resulting expression transforms in the right way under the modular group, and reproduces the known spectrum of these models.
• We also derive a formula for the partition function of deformed $CFT_2$ with non-vanishing chemical potential.