Nonlinear Langevin dynamics via holography

• Main Authors: Bidisha Chakrabarty, Joydeep Chakravarty, Soumyadeep Chaudhuri, Chandan Jana, R. Loganayagam, Akhil Sivakumar
• Format: Article
• Language: English
• Published: SpringerOpen 2020-01-01
• Series: Journal of High Energy Physics
• Subjects: Holography and quark-gluon plasmas; Quantum Dissipative Systems; AdS- CFT Correspondence
• Online Access: https://doi.org/10.1007/JHEP01(2020)165

Abstract In this work, we consider non-linear corrections to the Langevin effective theory of a heavy quark moving through a strongly coupled CFT plasma. In AdS/CFT, this system can be identified with that of a string stretched between the boundary and the horizon of an asymptotically AdS black brane solution. We compute the Feynman-Vernon influence phase for the heavy quark by evaluating the Nambu-Goto action on a doubled string configuration. This configuration is the linearised solution of the string motion in the doubled black brane geometry which has been proposed as the holographic dual of a thermal Schwinger-Keldysh contour of the CFT. Our expression for the influence phase passes non-trivial consistency conditions arising from the underlying unitarity and thermality of the bath. The local effective theory obeys the recently proposed non-linear fluctuation dissipation theorem relating the non-Gaussianity of thermal noise to the thermal jitter in the damping constant. This furnishes a non-trivial check for the validity of these relations derived in the weak coupling regime.