Structure function of holographic quark-gluon plasma: Sakai-Sugimoto model versus its non-critical version

TL;DR

This paper investigates the internal structure of holographic quark-gluon plasma using the Sakai-Sugimoto model and its non-critical version, analyzing how non-conformality influences structure functions in deep inelastic scattering.

Contribution

It compares the effects of non-conformality on plasma structure functions between the Sakai-Sugimoto model and a non-critical conformal model, revealing minimal impact of non-conformality on physical insights.

Findings

Non-conformality has little essential effect on plasma structure

Quantitative differences in structure functions depend on the model

Non-critical model results resemble conformal plasma behavior

Abstract

Motivated by recent studies of deep inelastic scattering (DIS) off the $\mathcal{N}=4$ super-Yang-Mills (SYM) plasma, holographically dual to $AdS_5\times S^5$ black hole, we in this note use the spacelike flavor current to probe the internal structure of one holographic quark-gluon plasma, which is described by the Sakai-Sugimoto model at high temperature phase (i.e., the chiral symmetric phase). The plasma structure function is extracted from the retarded flavor current-current correlator. Our main aim here is to explore the effect of non-conformality on these physical quantities. As usual, our study is under the supergravity approximation and the limit of large color number. Although the Sakai-Sugimoto model is non-conformal, which makes the calculations more involved than the well-studied $\mathcal {N}$=4 SYM case, the result seems to indicate that the non-conformality has little essential effect on the physical picture of the internal structure of holographic plasma, which is consistent with the intuition from the asymptotic freedom of QCD at high energy. While the physical picture underlying our investigation is same as the DIS off the $\mathcal {N}$=4 SYM plasma with(out) flavor, the plasma structure functions are quantitatively different, especially their scaling dependence on the temperature, which can be recognized as model-dependent. As a comparison, we also do the same analysis for the non-critical version of the Sakai-Sugimoto model which is conformal in the sense that it has a constant dilaton vacuum. The result for this non-critical model is much similar to the conformal $\mathcal{N}=4$ SYM plasma. We therefore attribute the above difference to the effect of non-conformality of the Sakai-Sugimoto model.