D-Brane Recoil Mislays Information

We discuss the scattering of a light closed-string state off a D-brane, taking into account quantum recoil effects on the latter, which are described by a pair of logarithmic operators. The light particle and D-brane subsystems may each be described by a world sheet with an external source due to the interaction between them. This perturbs each subsystem away from criticality, which is compensated by dressing with a Liouville field whose zero mode we interpret as time. The resulting evolution equations for the D-brane and the closed string are of Fokker–Planck and modified quantum Liouville type, respectively. The apparent entropy of each subsystem increases as a result of the interaction between them, which we interpret as the loss of information resulting from nonobservation of the other entangled subsystem. We speculate on the possible implications of these results for the propagation of closed strings through a dilute gas of virtual D-branes.