Finite coupling corrections to holographic predictions for hot QCD

TL;DR

The paper addresses how reliable holographic predictions for hot QCD-like plasmas remain when the 't Hooft coupling is finite rather than infinite. It collects and analyzes first-order finite-$\lambda$ corrections across thermodynamics, transport, and quasinormal mode spectra, and introduces a partial resummation scheme based on leading Type IIB $\alpha'$ corrections to stabilize results. The main finding is that QNM frequencies exhibit notable finite-$\lambda$ sensitivity at realistic couplings, but the resummation substantially mitigates this issue, while transport coefficients such as $\sigma$ and $\eta$ are less affected. Overall, the work demonstrates observable-dependent stability of holographic expansions and enhances confidence in applying AdS/CFT predictions to QGP physics at moderate coupling. $\lambda$-dependent corrections and a controlled resummation approach provide a practical path to more reliable holographic estimates in the 10–40 range.

Abstract

Finite 't Hooft coupling corrections to multiple physical observables in strongly coupled $N=4$ supersymmetric Yang-Mills plasma are examined, in an attempt to assess the stability of the expansion in inverse powers of the 't Hooft coupling $λ$. Observables considered include thermodynamic quantities, transport coefficients, and quasinormal mode frequencies. Although large $λ$ expansions for quasinormal mode frequencies are notably less well behaved than the expansions of other quantities, we find that a partial resummation of higher order corrections can significantly reduce the sensitivity of the results to the value of $λ$.

Figures (3)

• Figure 1: The first few QNM frequencies, divided by $2\pi T$, of the electromagnetic current operator for $\hat{q}=0$ (left) and $\hat{q}=1$ (right), evaluated at $\lambda=\infty$ (red squares) and $\lambda=1000$ (blue circles). The $\lambda = 1000$ results include the $O(\gamma)$ corrections, but no higher order contributions. Lines have been inserted merely to guide the eye.
• Figure 2: The first few QNM frequencies, divided by $2\pi T$, of the electromagnetic current operator for $\hat{q}=0$ (left figure) or $\hat{q}=1$ (right figure) at $\lambda = 1000$. Results obtained by directly solving the QNM equation at this value of $\lambda$ using spectral methods are shown as brown diamonds, while the red squares and blue circles show the same zeroth and first order results, respectively, previously displayed in fig. \ref{['fig1']}. Again, lines merely serve to guide the eye.
• Figure 3: The first few QNM frequencies, divided by $2\pi T$, for the shear channel of the stress-energy correlator, evaluated for $\hat{q}=0$ and $\lambda = 500$. Results obtained by directly solving the QNM equation at this value of $\lambda$ using spectral methods are shown as brown diamonds, while the red squares and blue circles show results truncated at zeroth and first order in $\gamma$, respectively. As before, lines merely serve to guide the eye.