Higher derivative holography and temperature dependence of QGP viscosities

TL;DR

The paper investigates higher-derivative corrections in 5D Einstein-dilaton holographic QCD (ihQCD/V-QCD) to reproduce the temperature-dependent transport observed in Bayesian analyses of heavy-ion collisions. By deriving horizon-based formulas for $\eta/s$ and $\zeta/s$ with four-derivative terms, they study how dilaton-dependent couplings $G(\Phi)$ can be tuned to match the Bayesian profiles, initially in perturbation theory. They find that a single Riemann-squared correction with a simple $G(\Phi)$ can fit the $\eta/s$ data only at the cost of large backreaction, breaking the perturbative regime, and that curvature corrections alone struggle to reproduce both $\eta/s$ and $\zeta/s$ across the Trajectum and Jetscape bands. A mild linear temperature dependence of $\eta/s$ improves some aspects but worsens the $\zeta/s$ fit, pointing to the need for additional curvature corrections (e.g., $R^2$, $R_{\mu\nu}^2$) or nonperturbative finite-coupling effects, as well as potential extensions to charge transport and electromagnetic-field effects. Overall, the work highlights the challenges of reconciling holographic four-derivative corrections with realistic QCD transport and suggests directions for more complete holographic models and consistency checks (causality, swampland constraints).

Abstract

Recent Bayesian analyses of heavy ion collision data have established a non-trivial temperature dependence of the shear and bulk viscosity per entropy. Motivated by this, we consider higher derivative corrections to realistic, bottom-up holographic models of quark-gluon plasma based on five-dimensional Einstein-dilaton theories and determine the dilaton potentials in the higher derivative terms by matching the Bayesian analyses. A byproduct of our analysis is the bulk viscosity that follows from the holographic V-QCD theory. Higher derivative corrections when treated perturbatively lead to tension with existing data. We investigate possible resolutions.

Figures (11)

• Figure 1: Posterior distribution for the shear viscosity to entropy ratio versus temperature for Trajectum (left) and Jetscape (right). For Trajectum the 90$\%$ confidence band is shown in blue and the dark blue curve is the mean. The gray area signifies the 90$\%$ confidence band for the prior distribution. For Jetscape see Figure \ref{['bulk visc figure']} for definition of the confidence bands.
• Figure 2: Posterior distribution for the bulk viscosity to entropy ratio versus temperature, with a 90$\%$ confidence band shown in blue, from Trajectum Giacalone:2023cet (left) and JetscapeJETSCAPE:2020mzn (right).
• Figure 3: Temperature in units of the confining scale $\Lambda$, as a function of the dilaton horizon value in V-QCD. The dotted line indicates the value of the critical temperature $T_c/\Lambda$, where the deconfining transition happens.
• Figure 4: Shear viscosity to entropy ratio for V-QCD with $G\left( \Phi \right)=1$. The blue area corresponds to the 90$\%$ confidence band for Trajectum while the green area corresponds to the 90$\%$ confidence band for Jetscape. The orange line shows the theoretical curve while the black line is $\eta/s=1/(4\pi)$ for reference. A curve that fits both Trajectum and Jetscape is obtained for $\beta=-0.05$.
• Figure 5: Best fit for the shear viscosity to entropy ratio for V-QCD with $G\left( \Phi \right)$ shown in Figure \ref{['VQCD dilaton potential and coupling']} ($\beta$ is set to 0.1). The orange line is the theoretical curve, which is compared with the 90$\%$ confidence band for Trajectum (blue area).