Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma (0812.2053v2)

Abstract: Using gauge/gravity duality, we study the creation and evolution of anisotropic, homogeneous strongly coupled $\mathcal N=4$ supersymmetric Yang-Mills plasma. In the dual gravitational description, this corresponds to horizon formation in a geometry driven to be anisotropic by a time-dependent change in boundary conditions.

• The paper employs gauge/gravity duality to link horizon formation with isotropization in strongly coupled supersymmetric Yang-Mills plasma.
• The paper presents numerical solutions of Einstein’s equations that reveal how anisotropic boundary conditions drive rapid equilibration with isotropization times tied to characteristic boundary changes.
• The paper demonstrates that the findings mirror thermalization dynamics observed in RHIC collisions, offering valuable insights into non-equilibrium plasma behavior.

Exploration of Far-From-Equilibrium Dynamics in Supersymmetric Yang-Mills Plasma

This paper is a detailed exploration of the dynamics involved in isotropization processes within a strongly coupled supersymmetric Yang-Mills (SYM) plasma, utilizing the framework of gauge/gravity duality. The research highlights the controlled paper of large-$N_c$, supersymmetric non-Abelian plasma, specifically focusing on the anisotropic, homogeneous states within this theoretical model. Such studies are motivated by the need to understand the dynamics underlying rapid isotropization observed in quasi-realistic simulations of quark-gluon plasma (QGP) systems, such as those produced at the Relativistic Heavy Ion Collider (RHIC).

Study Framework and Methodology

The authors utilize the gauge/gravity duality to draw parallels between horizon formation in a dual gravitational description and the isotropization processes in strongly coupled SYM plasma. In the gravitational framework, a time-dependent perturbation akin to a modifiable boundary condition influences the 5-dimensional bulk geometry. This is achieved through a prescribed metric that satisfies conditions of translation invariance, $O(2)$ rotational symmetry, and constant spatial volume, essentially driving anisotropization through manipulated spatial geometries ($B_0(t)$). The selected boundary conditions implicate horizon formation, the paper of which provides insights into the thermalization processes within the SYM plasma.

Numerical Solutions and Asymptotic Analysis

A core aspect of the paper involves solving Einstein’s equations numerically under boundary conditions determined by the stipulations of the imposed boundary metric. The symmetry and boundary constraints enable the authors to simplify the metric into a set of ordinary differential equations, effectively reducing the dynamics to calculable mathematical forms. The paper provides explicit detailing for the numerical procedure required to solve these differential equations and ascertain the resultant geometry evolution within the bulk.

During evolution, horizons form which entail the isotropization of non-vacuum states, transitioning to thermal equilibrium post perturbation. This scenario is intricately analyzed using power series expansions which reveal a solitary undetermined coefficient dictating the stress tensor’s involvement in the SYM plasma dynamics. Notably, the outcomes affirm that the dynamics governing isotropization can be probed effectively via gravitational perspectives.

Results

Key results demonstrate that isotropization time ($\tau_{\rm iso}$) scales with the characteristic time $\tau$, given specific temporal changes in the stress tensor driven by the boundary conditions. For variant initial conditions (characterized by different $c$ values in the metric function), the isotropization time remains on the order of the time scale of boundary change, hinting at intrinsic rapid plasma equilibration dynamics. The quantitative findings are consistent with isotropization times estimated in empirical studies of RHIC collisions, suggesting analogous processes in real-world QGP production.

A noteworthy computational figure shown in the paper represents the propagation of outgoing null radial geodesics and highlights the formation of apparent and event horizons. The true event horizon parts space into escapable and trapped geodesics, encapsulating the essence of isotropization in the bulk geometry view.

Theoretical and Practical Implications

This paper holds significant theoretical implications, positing that the characterization of plasma dynamics via gauge/gravity duality elucidates rapid thermalization observed in experimentally relevant non-Abelian plasma models. The control provided by supersymmetric theories advance our understanding of the relativistic hydrodynamic behavior at extreme conditions, potentially influencing future developments in non-equilibrium plasma theories, particularly for those using holographic methods.

The detailed approach to modeling anisotropic plasma conditions bolsters the feasibility of comprehending complex QCD systems, providing crucial inputs for simulations reliant on ideal hydrodynamic models.

In essence, this work constitutes a compelling investigation into the parallels between theoretical supersymmetric settings and real-world high-energy particle physics experiments, establishing a framework for future explorations of isotropization and relaxation dynamics in field theories at strong coupling.