Abstract
A relativistic fluid in 3+1 dimensions with a global U(1) symmetry admits nine independent static susceptibilities at the second order in the hydrodynamic derivative expansion, which capture the response of the fluid in thermal equilibrium to the presence of external time-independent sources. Of these, seven are time-reversal mathbbm{T} invariant and can be obtained from Kubo formulas involving equilibrium two-point functions of the energy-momentum tensor and the U(1) current. Making use of the gauge/gravity duality along with the aforementioned Kubo formulas, we compute all seven mathbbm{T} invariant second order susceptibilities for the mathcal{N} = 4 supersymmetric SU(Nc) Yang-Mills plasma in the limit of large Nc and at strong ’t-Hooft coupling λ. In particular, we consider the plasma to be charged under a U(1) subgroup of the global SU(4) R-symmetry of the theory. We present analytic expressions for three of the seven mathbbm{T} invariant susceptibilities, while the remaining four are computed numerically. The dual gravitational description for the charged plasma in thermal equilibrium in the absence of background electric and magnetic fields is provided by the asymptotically AdS5 Reissner-Nordström black brane geometry. The susceptibilities are extracted by studying perturbations to the bulk geometry as well as to the bulk gauge field. We also present an estimate of the second order transport coefficient κ, which determines the response of the fluid to the presence of background curvature, for QCD, and compare it with previous determinations made using different techniques.
Highlights
JHEP08(2021)108 the transport properties of the plasma in the absence of any external electric and magnetic fields, thereby restoring current conservation
A relativistic fluid in 3+1 dimensions with a global U(1) symmetry admits nine independent static susceptibilities at the second order in the hydrodynamic derivative expansion, which capture the response of the fluid in thermal equilibrium to the presence of external time-independent sources
As the strongly coupled N = 4 super-Yang-Mills plasma can be probed via holography, wherein its properties can be studied using a dual gravitational description, it provides a simpler and tractable model for the much more complicated dynamics of the quark-gluon plasma (QGP) which is hard to probe via direct computations [17]
Summary
SU(Nc) Yang-Mills theory is holographically dual to type IIB superstring theory on AdS5 × S5. In the limit where Nc → ∞ and the gauge theory is strongly coupled gY2 MNc → ∞, the dual bulk description simplifies considerably and is provided by classical type IIB supergravity. Where R is the Ricci scalar corresponding to the five-dimensional bulk metric GMN , and FMN = ∂M AN − ∂N AM is the field strength tensor for the bulk Abelian gauge field AM. The coefficient of the Chern-Simons term, α, has the numerical value 2/ 3, and is a measure of the strength of the chiral anomaly in the boundary super-Yang-Mills theory.. The metric γμν is induced by the bulk metric GMN on the conformal boundary of AdS5, and R is the associated fourdimensional boundary Ricci scalar. With ∇ being the covariant derivative and nM being the outward pointing normal vector to the boundary ∂M
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