Real-time correlators in warped AdS/CFT correspondence

TL;DR

This work extends real-time holographic techniques to warped AdS3 geometries, computing analytic retarded Green's functions for scalar and vector perturbations in spacelike-stretched and null warped black holes. By solving the perturbation equations (via hypergeometric and Kummer functions) and applying the Son–Iqbal prescription, the authors show that the gravity-derived $G_R$ matches the expected 2D CFT form with left- and right-moving weights and temperatures, including the associated quasi-normal modes and absorption cross sections. Extremal and chiral limits reveal consistent left- or right-moving sector behavior, underscoring the robustness of warped AdS/CFT and its potential relevance to non-relativistic AdS/CMT and Kerr/CFT contexts. A notable normalization discrepancy remains, pointing to subtle temperature-dependent factors in the precise holographic mapping, which invites further refinement.

Abstract

We study real-time correlators in the warped AdS/CFT correspondence. We apply the prescription used in the usual AdS/CFT correspondence and obtain the retarded Green's functions for the scalar and vector fields in the spacelike warped and the null warped black hole backgrounds. We find that the retarded Green's functions and the cross sections are well consistent with the predictions from dual CFT. Our results not only support strongly the conjectured warped AdS/CFT correspondence, but also show that the usual relativistic AdS/CFT prescription of obtaining the real-time correlators remain effective in more general backgrounds with anisotropic conformal infinity.