Effective field theory of dissipative fluids (1511.03646v3)

Abstract: We develop an effective field theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional $Z_2$ symmetry, to which we refer as the local KMS condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.

• The paper introduces a comprehensive framework that models dissipative fluids via a path integral formulation and fluctuating hydrodynamics.
• The paper recovers standard hydrodynamic equations as saddle-point solutions and proposes generalized Onsager relations for nonlinear interactions.
• The paper reveals emergent supersymmetry through invariant local KMS conditions and ghost fields, suggesting new avenues for quantum and non-equilibrium studies.

Overview of the Effective Field Theory of Dissipative Fluids

The paper entitled "Effective Field Theory of Dissipative Fluids" by Michael Crossley, Paolo Glorioso, and Hong Liu introduces a comprehensive framework for modeling the dynamics of dissipative fluids through an effective field theory (EFT). This approach capitalizes on the fluctuating hydrodynamics framework and is developed to systematically encompass nonlinear interactions of noise components.

Fundamentally, the paper investigates the gapless modes that originate from conserved quantities and articulates this through a path integral representation. The authors utilize mappings between a "fluid spacetime" and the physical spacetime, highlighting symmetries crucial to such formulations. One notable aspect of the theory is its applicability to nonlinear disturbances around various density matrices, including thermal ones.

A salient theoretical innovation in the paper is the introduction of additional symmetries, specifically the invariant local KMS (Kubo-Martin-Schwinger) condition, which traditionally constrains thermodynamic systems in equilibrium. The application to the full quantum regime reveals an emergent supersymmetry and a higher order derivative deformation, thereby offering insightful connections between thermal equilibrium and supersymmetric structures.

Numerical and Theoretical Results

Among the numerical results is the recovery of the standard hydrodynamic equations as saddle-point equations of the path integral, which validates the efficacy of the proposed formalism. Furthermore, the paper extends existing theories by proposing new constraints in the form of generalized Onsager relations, particularly notable at nonlinear levels of interaction.

The theoretical implications of this work are expansive. The authors surmise that introducing anti-commuting fields and a BRST-type symmetry ensures unitarity of time evolution within the low-energy effective action framework. This leads to a demonstration of emerging supersymmetry in the classical statistical limit, hinting at previously uncharted territory at the intersection of quantum field theory and statistical mechanics.

Speculative Connections and Future Directions

This work postulates several intriguing future directions, particularly in non-equilibrium systems and potentially chaotic regimes such as turbulence. Given the developed framework's capacity to model interactions at a full nonlinear level, we could reconsider classical phenomena through the lens of quantum field theory, potentially uncovering new symmetries or interaction principles relevant to high-energy physics or quantum gravity.

The quantum deformation of supersymmetry proposed by Liu and colleagues could have profound implications for theoretical models involving black holes, holography, and the AdS/CFT correspondence—particularly in the context of quantum gravitational fluctuations. Moreover, the introduction of ghost fields opens avenues for exploring the symmetries and topological aspects of stochastic dynamics, linking them with known phenomena described by Langevin dynamics.

Conclusion

In summary, the effective field theory of dissipative fluids proposed in the paper paves a novel path in understanding complex fluid dynamics through the lens of quantum field theories and fluctuating hydrodynamics. By integrating symmetry principles, particularly focusing on the invariant local KMS condition, the authors have contributed significantly to the toolkit available for modeling nonequilibrium phenomena. This paper not only challenges existing paradigms but also establishes a foundation for future exploration in both theoretical physics and applied disciplines employing fluid dynamics.