Hidden Conformal Symmetry and Emergent Holographic Structure in the AdS Teo Rotating Wormhole

TL;DR

This work shows that a horizonless rotating AdS Teo wormhole hosts an emergent $SL(2,\mathbb{R})$ conformal structure in its near-throat region, arising from a logarithmic tortoise coordinate and an exponential near-throat potential. The radial Klein–Gordon equation reduces to a quadratic Casimir problem, yielding a discrete quasinormal-mode spectrum $\omega_n = \omega_R - i\kappa\,(n+h)$ with conformal weight $h$, independent of horizon thermodynamics. Embedding the Teo wormhole in AdS provides a minimal holographic setup with two timelike boundaries and dual CFTs on each side, connected through the throat; QNMs appear as poles of retarded boundary correlators, and cross-boundary correlators are captured by the regulated geodesic length $L_{\rm reg}$ traversing the throat. The results establish a unified, analytic description of hidden conformal structure, spectral properties, and boundary observables in a rotating, horizonless AdS wormhole, highlighting horizon-independent mechanisms for conformal dynamics and holography.

Abstract

We study scalar perturbations of the rotating Teo wormhole embedded in asymptotically Anti-de Sitter (AdS) spacetime and demonstrate that the radial Klein Gordon equation exhibits an emergent conformal structure. The smooth traversable throat induces a logarithmic tortoise coordinate that allows the radial equation to be recast as the quadratic Casimir eigenvalue equation, paralleling the hidden conformal symmetry of the rotating Kerr black hole but arising here in a horizonless geometry. The AdS-Teo spacetime possesses two disconnected timelike AdS conformal boundaries that remain causally connected through the wormhole throat, in contrast to the two-sided eternal AdS black hole where horizons play a central role. Using the emergent conformal symmetry, we construct the near-throat generators, derive the effective potential, and obtain a discrete quasinormal-mode spectrum determined by regularity at the throat and standard AdS boundary conditions at infinity. The AdS embedding further enables a minimal holographic interpretation. As an explicit illustration, we compute an equal-time two-point function in the large-Delta (geodesic) limit from a regulated spacelike geodesic that traverses the wormhole, showing how the bulk geometry couples the two asymptotic boundaries. Together, these results provide a unified description of hidden conformal structure, spectral properties, and boundary correlators in a rotating, horizonless asymptotically AdS wormhole.