Abstract
This article is dedicated to the analysis of Weyl symmetry in the context of relativistic hydrodynamics. Here is discussed how this symmetry is properly implemented using the prescription of minimal coupling: ∂→∂+ωA. It is shown that this prescription has no problem to deal with curvature since it gives the correct expressions for the commutator of covariant derivatives.In hydrodynamics, Weyl gauge connection emerges from the degrees of freedom of the fluid: it is a combination of the expansion and entropy gradient. The remaining degrees of freedom, shear, vorticity and the metric tensor, are see in this context as charged fields under the Weyl gauge connection. The gauge nature of the connection provides natural dynamics to it via equations of motion analogous to the Maxwell equations for electromagnetism. As a consequence, a charge for the Weyl connection is defined and the notion of local charge is analyzed generating the conservation law for the Weyl charge.
Highlights
The holographic calculation of the η/s ratio in the N = 4 SYM plasma and the production of the Quark-Gluon plasma at RICH and LHC reveled the relativistic nature of this fluid and the scaling symmetry of the system [1, 2]
This article is organized as follows: section 2 is dedicated to analyze Weyl symmetry in a general scenario and the minimal coupling prescription is established, in section 3 is discussed the consequences of this symmetry in a hydrodynamical system, section 4 deals with the notion of local charge conservation for the Weyl gauge field and in section 5 are made some final comments
To repair the inhomogeneous terms of the hydrodynamical degrees of freedom it was introduced in [11] a Weyl covariant derivative that acts in the fields preserving their character of tensor density
Summary
The trace of Weyl symmetry comes either from the experimental bound on bulk viscosity and from the similarity of the η/s calculation in AdS/CFT to the experimental data This phenomenology calls attention to the importance of the dynamics of a relativistic fluid with Weyl invariance. The symmetric, transverse and traceless part of a contra-variant rank 2 tensor is T ab = These perturbations arise from the complete set of hydrodynamical degrees of freedom: the fluid entropy. Weyl symmetry constrains the dynamics of the fluid, reducing the number of transport coefficients in all orders. When this symmetry takes place expansion and entropy gradient are no longer allowed by symmetry in the gradient expansion, instead they combine forming the gauge connection. This article is organized as follows: section 2 is dedicated to analyze Weyl symmetry in a general scenario and the minimal coupling prescription is established, in section 3 is discussed the consequences of this symmetry in a hydrodynamical system, section 4 deals with the notion of local charge conservation for the Weyl gauge field and in section 5 are made some final comments
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