Holographic nonlinear hydrodynamics from AdS/CFT with multiple/non-Abelian symmetries

TL;DR

The paper develops a holographic framework for nonlinear hydrodynamics of strongly coupled plasmas with multiple and non-Abelian symmetries by solving bulk gravity in a derivative expansion. It applies the method to the STU model with U(1)^3 and to SU(2) gauge dynamics in arbitrary dimensions, obtaining explicit first-order transport data including diffusion and parity-violating terms from Chern-Simons couplings. It provides covariant expressions for the currents and demonstrates the universal shear-viscosity to entropy density ratio η/s = 1/(4π) in these setups, with non-Abelian diffusion structures extending Abelian results. The SU(2) sector is also embedded in M-theory via Tri-Sasakian compactifications to AdS_4, yielding concrete links between bulk couplings and boundary CFT data through the volume of X_7 and the four-dimensional Newton constant.

Abstract

We study viscous hydrodynamics of hot conformal field theory plasma with multiple/non-Abelian symmetries in the framework of AdS/CFT correspondence, using a recently proposed method of directly solving bulk gravity in derivative expansion of local plasma parameters. Our motivation is to better describe the real QCD plasma produced at RHIC, incorporating its U(1)^Nf flavor symmetry as well as SU(2)_I non-Abelian iso-spin symmetry. As concrete examples, we choose to study the STU model for multiple U(1)^3 symmetries, which is a sub-sector of 5D N=4 gauged SUGRA dual to N=4 Super Yang-Mills theory, capturing Cartan U(1)^3 dynamics inside the full R-symmetry. For SU(2), we analyze the minimal 4D N=3 gauged SUGRA whose bosonic action is simply an Einstein-Yang-Mills system, which corresponds to SU(2) R-symmetry dynamics on M2-branes at a Hyper-Kahler cone. By generalizing the bosonic action to arbitrary dimensions and Lie groups, we present our analysis and results for any non-Abelian plasma in arbitrary dimensions.