Hydrodynamic gradient expansion in gauge theory plasmas

Abstract: We utilize the fluid-gravity duality to investigate the large order behavior of hydrodynamic gradient expansion of the dynamics of a gauge theory plasma system. This corresponds to the inclusion of dissipative terms and transport coefficients of very high order. Using the dual gravity description, we calculate numerically the form of the stress tensor for a boost-invariant flow in a hydrodynamic expansion up to terms with 240 derivatives. We observe a factorial growth of gradient contributions at large orders, which indicates a zero radius of convergence of the hydrodynamic series. Furthermore, we identify the leading singularity in the Borel transform of the hydrodynamic energy density with the lowest nonhydrodynamic excitation corresponding to a `nonhydrodynamic' quasinormal mode on the gravity side.

• The paper demonstrates that the hydrodynamic gradient expansion in gauge theory plasmas diverges due to factorial growth, resulting in a zero radius of convergence.
• It employs the AdS/CFT correspondence and Borel transform to connect hydrodynamic and nonhydrodynamic modes in boost-invariant flows.
• The study’s insights pave the way for developing resummation techniques and refining phenomenological models in high-energy physics experiments.

Hydrodynamic Gradient Expansion in Gauge Theory Plasmas

The paper explores the intricacies of hydrodynamic gradient expansion within gauge theory plasmas, leveraging the framework of fluid-gravity duality. The authors focus on exploring the large-order behavior of the hydrodynamic series for a boost-invariant flow, calculated up to an unprecedented 240th order using the dual gravity description. This analysis reveals a factorial growth of gradient contributions at high orders, leading to the conclusion of a zero radius of convergence for the hydrodynamic series.

Key Insights

The main findings of the research are centered around two crucial phenomena observed in the gradient expansion:

1. Divergent Hydrodynamic Series: The study shows that the hydrodynamic gradient expansion, although a powerful tool in capturing the dynamics of many physical systems, inherently exhibits a zero radius of convergence. This is deduced from the factorial behavior of the energy density gradient coefficients obtained through the gauge-gravity duality approach.
2. Borel Transform and Nonhydrodynamic Modes: In attempting to handle the divergent series, the authors employ the technique of Borel transform, which highlights the existence of singularities associated with nonhydrodynamic quasinormal modes on the gravity side. Specifically, they identify the leading singularity in the Borel-transformed series with such a quasinormal mode, offering a new perspective into the link between hydrodynamic and nonhydrodynamic excitations.

Methodological Approach

The research smartly utilizes the AdS/CFT correspondence, a duality between a type of string theory defined on a hyperbolic space and a conformal field theory (CFT) on the boundary of this space, to express high-order hydrodynamic expansions through the dual gravity setup. This involves solving the Einstein equations with specific symmetries (Bjorken flow), which lead to the calculation of the stress tensor for a large number of derivatives.

Implications

Theoretical Implications

The findings provide a deeper understanding of the asymptotic nature of the hydrodynamic gradient expansion in strongly coupled systems, such as quark-gluon plasma. It places significant emphasis on the relevance of nonhydrodynamic modes, opening new avenues for exploring the non-perturbative aspects of fluid systems. Moreover, this work showcases the potential of fluid-gravity duality in elucidating complex behaviors in quantum field theories.

Practical Implications

In practical terms, the conclusions regarding the zero radius of convergence could impact how we utilize hydrodynamic expansions in modeling physical systems, particularly in understanding the dynamics of high-energy physics scenarios like those observed in heavy-ion collision experiments.

Future Directions

The research sets the stage for several future explorations:

• Resummation Techniques: There is a highlighted interest in developing and refining resummation techniques that can accommodate the divergent nature of the hydrodynamic series beyond the simplest Borel summation.
• Phenomenological Models: An integration of asymptotic series insights in refining phenomenological models used in experimental setups such as the RHIC and LHC could be pursued.
• Extended Duality Applications: Extending the fluid-gravity duality approach to other non-conformal or charged systems may offer further generalized insights into hydrodynamic series behaviors and their intricacies within varying physical contexts.

In summary, this paper significantly contributes to the theoretical understanding of hydrodynamics in gauge theory plasmas, presenting both challenges and opportunities in the field of theoretical physics, particularly concerning the interplay between hydrodynamic and nonhydrodynamic modes. This work not only underscores the factors limiting the applicability of hydrodynamic expansions but also elucidates potential pathways for addressing these limitations through innovative methodologies.