Effective dynamics of open 2D CFTs

TL;DR

This paper investigates the Lorentzian correlators of scalar primary operators in 2D CFTs, revealing how their structure is preserved during analytic continuation from Euclidean correlators, with implications for understanding open quantum system dynamics.

Contribution

It explicitly performs the analytic continuation of four-point functions in 2D CFTs, demonstrating the preservation of correlator structure in Lorentzian signature.

Findings

Analytic continuation preserves four-point correlator structure.

Convergence of OPE guarantees valid continuation.

Results connect Euclidean and Lorentzian correlators in 2D CFTs.

Abstract

We analyze the momentum-space representations of the Lorentzian correlators of scalar primary operators in an arbitrary 2D CFT. These correlators characterize the effective dynamics of open quantum systems. We derive the results from the Euclidean correlators through a systematic continuation to Lorentzian signature. Abstractly, it is known that the convergence of the OPE guarantees that the analytic continuation can be carried out also in the case of the four-point function. Here we explicitly perform such analytic continuation, showing that the general structure of the four-point correlator is preserved in Lorentzian signature.