Oscillating Strings and Non-Abelian T-dual Klebanov-Witten Background

TL;DR

This work investigates semiclassical oscillating strings in $AdS_5 \times T^{1,1}$ and in its non-Abelian T-dual along $SU(2)$. It derives explicit energy-oscillation-number relations for oscillations in AdS and in $T^{1,1}$, revealing a linear-like dispersion $\mathcal{E} \sim 2\mathcal{N} + 3\mathcal{J}$ with corrections, and shows that, for a finite range of T-dual coordinates, the non-Abelian T-dual background supports string states equivalent to those in the original Klebanov-Witten geometry. The study also analyzes oscillations along the T-dual directions, obtaining short-string energy expansions that depend on the T-dual coordinates, suggesting dual field theory operators with anomalous dimensions modulated by these coordinates. Overall, the results indicate that non-Abelian T-duality preserves a meaningful subsector of the string spectrum while modifying the full spectrum, and they point to operator structures in the dual $\mathcal{N}=1$ SCFT whose dimensions are sensitive to the T-dual data.

Abstract

We study oscillating string solutions in the Klebanov-Witten and its non-Abelian T-dual background dualised along an SU(2) isometry. We find the string energy as the function of oscillation number and angular momentum. We show that for a particular set of T-dual co-ordinates both the background have equal string states. We also study the string states where the strings are expanding and contracting in the T-dual co-ordinate direction. We expect the presence of the superconformal field theory dual operators whose anomalous dimensions depend on T-dual co-ordinate.