Penrose limit for holographic duals of JT over bar deformations

We explore bosonic string sigma models on warped BTZ x S-3 both in the plane wave as well as beyond plane wave limit. Using the light cone gauge, we obtain the corresponding Hamiltonian and therefore the spectrum associated with the pp wave strings. Our analysis reveals a constant shift in the spectrum arising as a result of TsT transformations along the isometries of the target space manifold. Imposing the energy positivity constraint on the CFT2 spectrum, we estimate an upper bound on the shift. We also estimate corrections as we go beyond the plane wave limit. Finally, we perform calculations using conformal gauge which reveals identical spectrum for the pp wave strings and thereby shows the equivalence between the two approaches.

Automated summary

In this study, bosonic string sigma models on warped BTZ x S-3 were explored both within and beyond the plane wave limit. By using the light cone gauge and conformal gauge, the corresponding Hamiltonian and spectrum associated with the pp wave strings were obtained, revealing a constant shift and corrections due to TsT transformations along the isometries of the target space manifold. The energy positivity constraint on the CFT2 spectrum was imposed to estimate an upper bound on the shift, and it was found that the spectra obtained using both approaches were identical, demonstrating equivalence.