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Effective field theory for hydrodynamics: thermodynamics, and the derivative expansion (1107.0731v1)

Published 4 Jul 2011 in hep-th, astro-ph.CO, gr-qc, nucl-th, and physics.flu-dyn

Abstract: We consider the low-energy effective field theory describing the infrared dynamics of non-dissipative fluids. We extend previous work to accommodate conserved charges, and we clarify the matching between field theory variables and thermodynamical ones. We discuss the systematics of the derivative expansion, for which field theory offers a conceptually clear and technically neat scheme. As an example, we compute the correction to the sound-wave dispersion relation coming from a sample second-order term. This formalism forms the basis for a study of anomalies in hydrodynamics via effective field theory, which is initiated in a companion paper.

Citations (244)

Summary

  • The paper introduces an effective field theory framework for hydrodynamics by reformulating conventional thermodynamics using a derivative expansion.
  • It provides a systematic dictionary matching field theory variables to thermodynamic quantities and details corrections to sound-wave dispersion relations.
  • The study lays the groundwork for future research on incorporating dissipative phenomena and extending models to include additional conserved charges.

An In-depth Analysis of Effective Field Theory for Hydrodynamics: Thermodynamics and the Derivative Expansion

The paper entitled "Effective Field Theory for Hydrodynamics: Thermodynamics, and the Derivative Expansion" by Sergei Dubovsky, Lam Hui, Alberto Nicolis, and Dam Thanh Son, presents a profound analysis of the effective field theory (EFT) framework applied to hydrodynamics. This work extends previous models to accommodate conserved charges and provides clarity in matching field theory variables to thermodynamic quantities, offering a systematic approach to the derivative expansion specifically tailored for non-dissipative fluids.

Overview and Theoretical Foundation

At the core of this paper is the formulation of hydrodynamics as an effective field theory. This perspective leverages the inherent symmetries of fluid systems, much akin to how chiral Lagrangians describe Goldstone bosons. The authors propose that hydrodynamics, though traditionally distinct from field theories, can be recast into this language by determining the symmetries of the fluid and then constructing the most general EFT consistent with these symmetries and the derivative expansion.

Technical Approach and Derivative Expansion

The derivative expansion serves as a natural perturbation scheme in effective field theories. The paper carefully delineates the procedure for scaling this up to higher orders. One of the main contributions is the establishment of a robust dictionary that links field theoretical constructs to traditional thermodynamic variables. Furthermore, the work exemplifies the systematic inclusion of higher-order corrections, offering rigorous prescriptions for aligning field definitions between theoretical frameworks and conventional hydrodynamic parlance.

For instance, the paper provides significant insights into the constraint imposed by symmetries, such as the chemical shift symmetry for fluids with conserved charges. Through detailed derivations, it discusses the sound-wave dispersion relation corrections, an example of tangible outcomes from second-order terms in the derivative expansion.

Implications and Future Directions

While the paper primarily addresses non-dissipative dynamics, it lays the groundwork for extending effective field theory methods to account for dissipative phenomena, a potential yet complex challenge. The authors suggest that coupling fluid Goldstones with a separate soft sector could mimic dissipative effects seen in holographic models, a subject earmarked for future research.

Beyond the immediate scope of hydrodynamics, this framework could yield constraints akin to the null energy condition or limits on anomaly coefficients, proving fruitful in broader physical contexts. Additionally, the approach allows expansion into models encompassing more extensive conserved quantities and alternative symmetry settings, introducing avenues to conceptualize novel systems.

Conclusion

In conclusion, Dubovsky et al.'s work critically enhances the theoretical toolkit for hydrodynamics by embedding it within the well-established structure of effective field theory. This paper not only provides a distinctive viewpoint on fluid dynamics but also underscores the versatility and efficacy of field theory in elucidating complex systems characterized by symmetries and conserved charges. As scholars continue to explore the practical and theoretical implications, this work stands as a significant reference point in the ongoing development of hydrodynamic theory.