Effective dynamics of open 2D CFTs

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.