Finite-Time Doppler Covariance Spectroscopy in the AdS/CFT correspondence

Abstract

From a holographic perspective, we formulate an exact finite-duration covariance framework that resolves chirality in the AdS/CFT correspondence. In a rotating BTZ black hole spacetime, relative motion between two boundary controls converts sum-frequency matching on the compact boundary cylinder into discrete velocity resonances indexed by the angular momentum of the scalar field. Because the complete real-control covariance also contains difference-frequency sectors, a two-setting quadrature cycle cancels them and reconstructs the resonant pair contribution from complete positive-semidefinite covariance matrices. For an isolated angular mode, reconstructed pair responses at opposite resonance velocities sample the boundary spectrum at opposite angular momentum and a common control-selected frequency. Their normalized contrast cancels reflection-symmetric control factors and the state-independent operator normalization, yielding a finite-linewidth estimator of intrinsic bath chirality. For a smooth bath spectrum, the bias from common centered even narrowing windows begins at quadratic order in linewidth, extending the protection beyond Gaussian sampling. An explicit real-projection leakage bound controls contamination from neighboring modes. Long-pulse calculations with the exact BTZ spectrum verify phase-cycle reconstruction and quadratic linewidth scaling. Bath-weighted calculations with exact truncated transfer amplitudes establish convergence to this baseline. Under the default controls, the first two nonzero angular modes support extraction from the complete angular sum and reconstruct the BTZ rotation parameter with subpercent deterministic bias. The framework thus separates control-induced resonance kinematics from intrinsic bath chirality and converts finite-time covariance data into a quantitative estimate of the rotating BTZ black hole.