Penrose limit for holographic duals of $ J\bar{T} $ deformations

TL;DR

This paper studies string models on warped geometries related to $ Jar{T} $ deformations, analyzing spectra in plane wave limits and beyond, revealing spectrum shifts due to TsT transformations and confirming approach equivalence.

Contribution

It provides a detailed spectrum analysis of warped $ BTZ \times S^3 $ string models in both plane wave and beyond limits, highlighting the effects of TsT transformations and approach equivalence.

Findings

Spectrum shift due to TsT transformations.

Upper bound on spectrum shift from energy positivity.

Equivalence of conformal and light cone gauge spectra.

Abstract

We explore bosonic string sigma models on warped $ BTZ\times 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 CFT$_2 $ 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.