Finite coupling corrections to holographic predictions for hot QCD

Sebastian Waeber,Laurence G Yaffe,Aleksi Vuorinen,Andreas Schäfer

doi:10.1007/jhep11(2015)087

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 $\lambda$. Observables considered include thermodynamic quantities, transport coefficients, and quasinormal mode frequencies. Although large $\lambda$ 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 $\lambda$.

Highlights

JHEP11(2015)087 shock waves [34,35,36,37], and collisions of fully localized shock waves resembling Lorentz contracted nuclei [38, 39]
The strong coupling, large Nc limit of N = 4 SYM, to which gauge/gravity duality applies, may be viewed as a three-step deformation of QCD: (i) the fundamental representation quarks of QCD are replaced by a collection of adjoint representation matter fields, both fermions and scalars, thereby turning QCD into N = 4 SYM, (ii) the ’t Hooft coupling λ ≡ gY2 M Nc, which no longer runs with energy scale in N = 4 SYM, is tuned to very large values, and (iii) the gauge group rank, Nc, is sent to infinity
Our examination of finite-λ corrections to holographic results for thermal quantities is motivated by an obvious desire to understand more clearly the applicability of gauge/gravity duality to the physics of quark-gluon plasma as produced in real heavy ion collisions

Summary

First order corrections: collected results

Considerable prior work exists examining finite-λ corrections to holographic results. A priori, it is not clear whether the above behavior of the QNM frequencies is due to an abnormally large first term in an otherwise well-behaved expansion, or whether the quantities in question are sensitive to finite coupling corrections, so that their expansions in γ have an abnormally small range of utility. Deciding between these alternatives would, in principle, require an all orders determination of the strong coupling expansion, which is far beyond the reach of present day technology. This investigation should be helpful in inferring the range of utility of the above first order results

Finite coupling corrections to correlators and QNMs

Current-current correlator

Stress-energy correlator

Findings

Conclusions