Hydrodynamics with Triangle Anomalies (0906.5044v2)

Abstract: We consider the hydrodynamic regime of theories with quantum anomalies for global currents. We show that a hitherto discarded term in the conserve current is not only allowed by symmetries, but is in fact required by triangle anomalies and the second law of thermodynamics. This term leads to a number of new effects, one of which is chiral separation in a rotating fluid at nonzero chemical potential. The new kinetic coefficients can be expressed, in a unique fashion, through the anomalies coefficients and the equation of state. We briefly discuss the relevance of this new hydrodynamic term for physical situations, including heavy ion collisions.

• The paper introduces a novel kinetic term that incorporates triangle anomalies into hydrodynamic equations, enabling chiral separation in rotating fluids.
• It employs gauge/gravity duality computations to confirm non-zero anomaly-induced coefficients in N=4 super-Yang-Mills plasma contexts.
• The analysis highlights implications for quark-gluon plasma studies and heavy-ion collisions, prompting further research into quantum anomaly impacts on fluid dynamics.

Hydrodynamics with Triangle Anomalies: An Analytical Overview

The research article titled "Hydrodynamics with Triangle Anomalies" by Dam T. Son and Piotr Sur´ówka investigates an important extension to the framework of relativistic hydrodynamics by incorporating quantum anomalies for global currents. The paper thoroughly analyzes the interplay between hydrodynamics and anomalies, particularly focusing on the implications of triangle anomalies in a relativistic fluid system. The paper presents a detailed formulation of how quantum anomalies, specifically triangle anomalies, influence hydrodynamic equations and proposes modifications necessary for their inclusion in the theoretical framework.

Summary of Results

At its core, the paper seeks to elucidate the effects of triangle anomalies on hydrodynamics by introducing a new kinetic term in the constitutive equations of the fluid, expressed as:

$$j^\mu = n u^\mu - \sigma T (g^{\mu\nu} + u^\mu u^\nu) \partial_\nu T + \xi \omega^\mu$$

where $$\omega^\mu = \frac{1}{2} \epsilon^{\mu\nu\lambda\rho}u_\nu \nabla_\lambda u_\rho$$ represents the fluid's vorticity. The introduction of the new kinetic coefficient $\xi$, which is directly linked to anomalies, leads to a novel phenomenon termed "chiral separation" in a rotating fluid at a non-zero chemical potential.

The authors establish that this additional term does not violate the second law of thermodynamics; rather, it is required by it. They utilize gauge/gravity duality computations to provide further support by showing non-zero values of $\xi$ in N = 4 super-Yang-Mills plasma contexts and link $\xi$ to the anomaly coefficient $C$ through:

$$\xi = C \left(\frac{2}{3} - \frac{3n}{\epsilon + P}\right)$$

where $\epsilon$ and $P$ are the energy density and pressure of the fluid, respectively.

Implications and Future Directions

The findings hold significant implications for theoretical and practical domains such as quark-gluon plasma studies where relativistic flows are pertinent, and the small mass of quarks amplifies anomaly effects. Further, in scenarios like heavy ion collisions, accounting for triangle anomalies could lead to a more accurate depiction of dynamics. A specific phenomenological exploration is made in connection with the chiral magnetic effect, relevant in explaining charge asymmetries in heavy-ion collision outcomes.

The modification to hydrodynamic equations, illuminated by this paper, represents a crucial step in understanding macroscopic manifests of quantum effects, suggesting uniformity across theories with gravitational interaction duals. There is a consideration for extending these formulations to multiple U(1) charges, indicating the breadth of potential applications.

Further research could focus on the microscopic origins of the vorticity-induced current, particularly in weakly coupled theories. Investigations into similar anomaly-induced effects in dense astrophysical bodies or early universe conditions with high lepton densities could provide valuable insights.

Conclusion

In summary, the paper brings to light a critical modification to the relativistic hydrodynamic theories mandated by triangle anomalies. The comprehensive analytic constructs and demonstrations rooted in both traditional hydrodynamics and holographic models extend our understanding of quantum anomaly effects in high-energy physics contexts. This foundational work paves the way for subsequent exploration of anomaly impacts in diverse physical settings across the realms of theoretical physics.