Bulk viscosity of gauge theory plasma at strong coupling (0708.3459v2)

Abstract: We propose a lower bound on bulk viscosity of strongly coupled gauge theory plasmas. Using explicit example of the N=2^* gauge theory plasma we show that the bulk viscosity remains finite at a critical point with a divergent specific heat. We present an estimate for the bulk viscosity of QGP plasma at RHIC.

• The paper proposes a new lower bound for the bulk-to-shear viscosity ratio in strongly coupled gauge theories using gauge/gravity duality.
• It employs numerical and holographic analyses of non-conformal plasmas, including 2* theories and scenarios from Dp-brane models.
• Results show that despite phase transitions and diverging specific heat, the bulk viscosity remains finite, offering new insights into QGP dynamics.

Bulk Viscosity of Gauge Theory Plasma at Strong Coupling

The paper "Bulk viscosity of gauge theory plasma at strong coupling" by Alex Buchel provides a detailed analysis of bulk viscosity within strongly coupled gauge theories, with specific attention to non-conformal plasmas and implications for the quark-gluon plasma (QGP) experiments like those conducted at RHIC. The author applies the framework of gauge/gravity duality, building on the success of holographic theories in describing thermodynamic and dynamic properties of strongly coupled QCD-like plasma.

The author begins by situating the work within the context of finite temperature gauge theories, whose properties have been elucidated via their dual descriptions in string theory black holes. A significant motivation for the paper arises from the universality of certain features in strongly coupled gauge theories, such as the well-known ratio of shear viscosity $\eta$ to entropy density $s$, proposed by Kovtun, Son, and Starinets (KSS) to have a lower bound of $1/4\pi$. This bound has motivated further exploration into the dynamics of such systems, specifically the behavior of bulk viscosity $\zeta$.

Buchel proposes a lower bound on the ratio of bulk viscosity to shear viscosity, $\zeta/\eta$, in strongly coupled gauge theories. The conjectured bound is expressed as:

$$\frac{\zeta}{\eta} \geq 2 \left(\frac{1}{p} - c_s^2\right)$$

where $p$ is the number of spatial dimensions and $c_s$ is the speed of sound. The dynamic nature of this bound reflects that both $\zeta/\eta$ and $c_s$ vary with temperature. The paper asserts that this bound should hold over the entire temperature range of the gauge theory plasma.

Evidence for this bound is presented through multiple lines of reasoning. Firstly, it highlights scenarios where the bound is saturated, such as plasmas holographically dual to near-extremal stacks of Dp-branes, and in Little String Theory. These scenarios, defined by specific brane configurations, offer a robust testing ground for the theoretical bound under consideration.

Additionally, the paper analyzes non-conformal plasmas at high temperatures - an area of significant interest given the relevance to QGP studies. Here, the author deduces the satisfaction of the proposed bound in cascading theories and $=2^*$ gauge theories when expanded to regimes beyond conformality. The numerical results indicate that while the bound holds, saturation is typically not observed, suggesting intricate dependencies on underlying microscopic parameters that warrant further investigation.

Crucially, this paper provides an in-depth exploration of $=2^*$ gauge theory plasma, evaluating its viscosity across diverse temperature ranges and mass deformation parameters. Of particular importance is the case with no fermionic masses, where the system presents a phase transition characterized by a vanishing speed of sound. Interestingly, despite a divergence in specific heat at the critical point, the bulk viscosity remains finite, reinforcing the potential universality of the derived bound for dynamically complex regimes.

Lastly, the author ventures a speculative estimate for QGP viscosity constrained within the operational conditions akin to those at RHIC. Given that RHIC operates near critical points similar to the observed $=2^*$ phenomena, these theoretical models offer promising new directions for understanding QGP behavior in experimental contexts.

In conclusion, the paper presents a compelling hypothesis surrounding the bulk viscosity of strongly coupled gauge theories, substantiated with holographic methods and numerical analysis. Theoretical advancements such as these promise to bridge gaps between abstract string theory predictions and tangible experimental observations, albeit with lingering queries regarding the fundamental principles governing non-universal features. Future research could expand to alternative holographic models, seeking empirical validation and pursuing a deeper comprehension of QGP thermodynamics at critical transitions.