Open quantum systems and Schwinger-Keldysh holograms
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Springer
Received: June 9, 2020 Accepted: July 9, 2020 Published: July 31, 2020
Open quantum systems and Schwinger-Keldysh holograms
a
International Centre for Theoretical Sciences (ICTS-TIFR), Tata Institute of Fundamental Research, Shivakote, Hesaraghatta, Bangalore 560089, India b Center for Quantum Mathematics and Physics (QMAP) Department of Physics, University of California, Davis, CA 95616 U.S.A.
E-mail: [email protected], [email protected], [email protected] Abstract: We initiate the study of open quantum field theories using holographic methods. Specifically, we consider a quantum field theory (the system) coupled to a holographic field theory at finite temperature (the environment). We investigate the effects of integrating out the holographic environment with an aim of obtaining an effective dynamics for the resulting open quantum field theory. The influence functionals which enter this open effective action are determined by the real-time (Schwinger-Keldysh) correlation functions of the holographic thermal environment. To evaluate the latter, we exploit recent developments, wherein the semiclassical gravitational Schwinger-Keldysh saddle geometries were identified as complexified black hole spacetimes. We compute real-time correlation functions using holographic methods in these geometries, and argue that they lead to a sensible open effective quantum dynamics for the system in question, a question that hitherto had been left unanswered. In addition to shedding light on open quantum systems coupled to strongly correlated thermal environments, our results also provide a principled computation of Schwinger-Keldysh observables in gravity and holography. In particular, these influence functionals we compute capture both the dissipative physics of black hole quasinormal modes, as well as that of the fluctuations encoded in outgoing Hawking quanta, and interactions between them. We obtain results for these observables at leading order in a low frequency and momentum expansion in general dimensions, in addition to determining explicit results for two dimensional holographic CFT environments. Keywords: AdS-CFT Correspondence, Black Holes, Thermal Field Theory ArXiv ePrint: 2004.02888
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)242
JHEP07(2020)242
Chandan Jana,a R. Loganayagama and Mukund Rangamanib
Contents 1 Introduction
1
2 grSK: the gravitational Schwinger-Keldysh saddle
8 12 12 15
4 Scalar propagation in grSK geometries 4.1 Scalar boundary to bulk propagators in grSK geometry 4.2 Propagators in d = 2 4.3 Propagators in d > 2: gradient expansion
17 18 20 21
5 Influence functionals 5.1 Quadratic effective action 5.2 Interactions: contact self-interaction 5.2.1 Influence functionals in the advanced-retarded basis 5.2.2 Influence functionals in the average-difference basis
22 23 26 27 30
6 Stochastic description of the open effective field theory
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7 Discussion
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A Gradient expansion on the grSK contour
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B Gradient exp
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