Out-of-Time-Order-Correlators in Holographic EPR pairs

In this note, we investigate the out-of-time-order correlators (OTOCs) for quantum fields in a holographic framework describing Einstein-Podolsky-Rosen (EPR) pairs. We compute the four-point and six-point OTOCs using the gravity dual, represented by the string worldsheet theory in Anti-de Sitter (AdS) space. These correlators quantify the rate at which information is scrambled, leading to the disentanglement of the EPR pair. We demonstrate consistency between two approaches for calculating OTOCs: the holographic influence functional on worldsheets perturbed by shock waves, and the worldsheet scattering in the eikonal approximation. We show that the OTOCs exhibit an initial phase of exponential growth, with six-point correlators indicating a marginally longer scrambling time compared to four-point correlators.

💡 Research Summary

In this paper the authors investigate out‑of‑time‑order correlators (OTOCs) for quantum fields living on a holographic Einstein‑Podolsky‑Rosen (EPR) pair. The holographic model consists of a fundamental string in AdS(_{d+1}) whose two endpoints are anchored on the AdS boundary and accelerate uniformly in opposite directions. This motion induces on the string world‑sheet a two‑sided AdS black‑hole geometry (a wormhole) with temperature (\beta=2\pi b).

The first part of the work introduces shock‑wave perturbations on the world‑sheet. A massless pulse emitted from the left boundary propagates along the (U\simeq0) horizon and produces a shift (\gamma) in the (V) coordinate. By taking a double‑scaling limit (the pulse energy is taken to zero while the boost factor diverges) a finite (\gamma) is retained. Using the holographic influence functional the authors compute the two‑point cross‑correlator (G_{LR}(t,t’)) between operators attached to the left and right particles. They then identify the state (|\gamma=0\rangle) with the thermal field‑double (TFD) state and show that (G_{LR}) is precisely the thermal OTOC analytically continued to complex time (-\beta/2). This establishes that the shock‑wave background encodes the same information as a standard OTOC.

The second part adopts a completely different technique: eikonal scattering on the world‑sheet. Small fluctuations of the string, denoted (q(U,V)), and of the operator insertion field (q_W(U,V)) are Fourier‑transformed to momentum space wavefunctions (\phi_i(p)). The initial and final states of the scattering process are built from these wavefunctions. In the high‑energy (eikonal) limit the scattering amplitude reduces to a simple phase (\exp