Abstract
We outline a universal Schwinger-Keldysh effective theory which describes macroscopic thermal fluctuations of a relativistic field theory. The basic ingredients of our construction are three: a doubling of degrees of freedom, an emergent abelian symmetry associated with entropy, and a topological (BRST) supersymmetry imposing fluctuationdissipation theorem. We illustrate these ideas for a non-linear viscous fluid, and demonstrate that the resulting effective action obeys a generalized fluctuation-dissipation theorem, which guarantees a local form of the second law.
Highlights
The construction we describe in the main text explicitly illustrates that the broad principles laid out in [32] suffice to construct an effective field theory of dissipative hydrodynamics
Obtaining an effective action for dissipative hydrodynamics, as we have presaged in §1, is interesting for understanding the dynamics of quantum fields in generic non-equilibrium settings, but has implications for other areas of physics
The advantage hydrodynamics has is that the phenomenological theory is very well understood and one has a clear target to attain to declare success
Summary
We begin by examining the fundamental symmetries of a SK path integral. Given an initial density matrix ρinitial of a QFT, we define the SK generating functional. Apart from the usual action on σa, CPT exchanges θ ↔ θ and acts as an R-parity on the superspace This is necessitated by our requirement that the θθ component of the superfields be identified with difference operators. Inspired by our previous studies of the structural consequences of the second law in relativistic fluids, we had advocated a solution to this conundrum in terms of an emergent U (1)T gauge invariance [12, 13, 32] This KMS symmetry acts on the fields by thermal translations. Given the low-energy superfields Y, the theory of macroscopic fluctuations is given as the general superspace action invariant under U (1)T gauge transformations. A complete story involves explaining how the equivariant construction of U (1)T dynamics works and will appear soon in our companion paper [42].5
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