Strongly coupled $\mathcal{N}=4$ super Yang-Mills plasma on the Coulomb branch II: Transport coefficients and hard probe parameters

TL;DR

This paper investigates the transport properties and hard probe parameters of strongly coupled $ ext{N}=4$ super Yang-Mills plasma on the Coulomb branch using supergravity duals, revealing temperature-dependent behaviors and differences between black hole branches.

Contribution

It provides the first detailed analysis of transport coefficients and hard probe parameters for $ ext{N}=4$ cSYM on the Coulomb branch at finite temperature using rotating black brane solutions.

Findings

Bulk viscosity to entropy ratio peaks near critical temperature for large black holes.

Transport coefficients increase with temperature for large black holes, approaching conformal values.

For small black holes, transport coefficients decrease with temperature, showing contrasting behavior.

Abstract

We study $\mathcal{N} = 4$ super Yang-Mills theory on the Coulomb branch (cSYM) by using its Type IIB supergravity dual. We compute the transport coefficients, and hard probe parameters of $\mathcal{N} = 4$ cSYM at finite temperature $T$. We use the rotating black 3-brane solution of Type IIB supergravity with a single non-zero rotation parameter $r_{0}$ after analytically continuing $r_{0}\rightarrow -ir_{0}$, and in an ensemble where the Hawking temperature $T$ and a scalar condensate $<\mathcal{O}>\sim r_{0}^4$ are held fixed. We find that the bulk viscosity to entropy density ratio of the large black hole branch decreases with temperature and has a maxima around the critical temperature $T_{c}$ while, for the small black hole branch, it increases with temperature. The other transport coefficients and parameters of hard probes, such as the conductivity, jet quenching parameter, drag force, and momentum diffusion coefficients of the large black hole branch increase with temperature and asymptote to their conformal value while, for the small black hole branch, they decrease with temperature.