An entropy current in superspace

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 functional 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. Contents

Section: Discussionmentioning

confidence: 99%

Nonlinear Langevin dynamics via holography

Chakrabarty

Chakravarty

Chaudhuri

et al. 2020

“…An effective action and an entropy current for diffusion using Schiwnger-Keldysh techniques at finite have been constructed in ref. [20,32]. Extending these results to the full fluid dynamics case is problematic and one needs to rely on an approximation where quantum fluctuations are neglected.…”

Section: Discussionmentioning

confidence: 99%

Holographic Schwinger-Keldysh effective field theories

Heller

Pinzani-Fokeeva

2019

Self Cite

We construct a holographic dual of the Schwinger-Keldysh effective action for the dissipative low-energy dynamics of relativistic charged matter at strong coupling in a fixed thermal background. To do so, we use a mixed signature bulk spacetime whereby an eternal asymptotically anti-de Sitter black hole is glued to its Euclidean counterpart along an initial time slice in a way to match the desired double-time contour of the dual field theory. Our results are consistent with existing literature and can be regarded as a fully-ab initio derivation of a Schwinger-Keldysh effective action. In addition, we provide a simple infrared effective action for the near horizon region that drives all the dissipation and can be viewed as an alternative to the membrane paradigm approximation.

“…Note added: While this paper was nearing completion, [53] appeared on the arXiv, which has some overlap with this work (especially elements of §4).…”

Section: A Brief History Of Hydrodynamic Effective Field Theoriesmentioning

confidence: 94%

Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow

Haehl

Loganayagam

Rangamani

2018

We present a detailed and self-contained analysis of the universal Schwinger-Keldysh effective field theory which describes macroscopic thermal fluctuations of a relativistic field theory, elaborating on our earlier construction [1]. We write an effective action for appropriate hydrodynamic Goldstone modes and fluctuation fields, and discuss the symmetries to be imposed. The constraints imposed by fluctuation-dissipation theorem are manifest in our formalism. Consequently, the action reproduces hydrodynamic constitutive relations consistent with the local second law at all orders in the derivative expansion, and captures the essential elements of the eightfold classification of hydrodynamic transport of [2]. We demonstrate how to recover the hydrodynamic entropy and give predictions for the non-Gaussian hydrodynamic fluctuations.The basic ingredients of our construction involve (i) doubling of degrees of freedom a la Schwinger-Keldysh, (ii) an emergent gauge U (1) T symmetry associated with entropy which is encapsulated in a Noether current a la Wald, and (iii) a BRST/topological supersymmetry imposing the fluctuation-dissipation theorem a la Parisi-Sourlas. The overarching mathematical framework for our construction is provided by the balanced equivariant cohomology of thermal translations, which captures the basic constraints arising from the Schwinger-Keldysh doubling, and the thermal Kubo-Martin-Schwinger relations. All these features are conveniently implemented in a covariant superspace formalism. An added benefit is that the second law can be understood as being due to entropy inflow from the Grassmann-odd directions of superspace. arXiv:1803.11155v2 [hep-th] 10 Sep 2018 J Fixing the worldvolume connection 103 K Superspace expansion of further fields in the MMO limit 108 -1 -Recently an answer to this question has emerged, mainly in the context of treating fluid dynamics as an effective theory [2,23]. It was conjectured the correct local principle to enforce is to demand an emergent 'entropic' gauge symmetry dubbed U (1) T , which in real time provides the correct analytic continuation of the Euclidean periodicity. Its gauge current is the entropy current (this statement can be thought of as a generalization of Wald's idea that equilibrium entropy is a Noether charge [24]). This emergent KMS gauge symmetry can be understood in terms of the topological structure of the Schwinger-Keldysh construction. In particular, it was argued in [5] that the additional constraints coming from KMS invariance lead to a quartet of operations that act on the Schwinger-Keldysh super-operator algebra. Two of these are Grassmann odd, thermal counterparts of the BRST charges, Q KM S , Q KM S and the two others are Grassmann even generators Q 0 KM S , L KM S . 2 One can intuitively understand the thermal generators in the following fashion. For a thermal system one can view real time dynamics as occurring on a background spacetime that admits a fibration by a thermal circle. Recall that we are used to analyzing equilibrium dynami...