Real-time response in AdS/CFT with application to spinors

TL;DR

This work provides an intrinsic Lorentzian formulation for real-time AdS/CFT correlators by analytic continuation from the Euclidean prescription, showing that the boundary canonical momentum encodes the response $\langle \mathcal{O} \rangle$ and enabling a practical calculation of retarded functions. It extends the framework to spinor operators, detailing the treatment of first-order Dirac equations and the appropriate boundary conditions, and derives explicit results in exact backgrounds. Two solvable examples, pure AdS and BTZ, illustrate the method: the fermionic retarded correlators are expressed in closed form via gamma-function structures and reproduce the expected pole spectra corresponding to conformal weights $(h_L,h_R)$ and thermal data. The approach clarifies the role of horizon data for transport and opens avenues for studying finite-temperature/density fermionic dynamics and potential holographic probes of Fermi surfaces.

Abstract

We discuss a simple derivation of the real-time AdS/CFT prescription as an analytic continuation of the corresponding problem in Euclidean signature. We then extend the formalism to spinor operators and apply it to the examples of real-time fermionic correlators in CFTs dual to pure AdS and the BTZ black hole.