Gauged supergravity from type IIB string theory on Y^{p,q} manifolds

TL;DR

Buchel and Liu construct a consistent nonlinear Kaluza-Klein reduction of Type IIB string theory on Sasaki–Einstein manifolds $Y^{p,q}$ to five-dimensional minimal ${\cal N}=2$ gauged supergravity, enabling holographic study of $U(1)_R$-charged plasmas. They obtain explicit reductions for $T^{1,1}$ and general $Y^{p,q}$, identify the graviphoton as the $U(1)_R$ gauge field, and analyze the thermodynamics and hydrodynamics of the corresponding $R$-charged black holes. They show that the shear viscosity to entropy density ratio remains universal, $\eta/s = 1/(4\pi)$, even at nonzero $R$-charge chemical potential, and compute the sound speed $c_s^2 = 1/3$. They conjecture that this universality extends to a broad class of strongly coupled gauge theory plasmas with gravity duals, with implications for RG flows and realistic QCD-like plasmas.

Abstract

We first construct a consistent Kaluza-Klein reduction ansatz for type IIB theory compactified on Sasaki-Einstein manifolds Y^{p,q} with Freund-Rubin 5-form flux giving rise to minimal N=2 gauged supergravity in five dimensions. We then investigate the R-charged black hole solution in this gauged supergravity, and in particular study its thermodynamics. Based on the gauge theory/string theory correspondence, this non-extremal geometry is dual to finite temperature strongly coupled four-dimensional conformal gauge theory plasma with a U(1)_R-symmetry charge chemical potential. We study transport properties of the gauge theory plasma and show that the ratio of shear viscosity to entropy density in this plasma is universal. We further conjecture that the universality of shear viscosity of strongly coupled gauge theory plasma extends to nonzero R-charge chemical potential.