Asymptotic Freedom for Holographic Energy Correlators

TL;DR

The paper investigates holographic energy correlators in a 5D model that incorporates asymptotic freedom and confinement by introducing a running coupling through a warp-factor deformation. By solving for shockwave profiles in this geometry, the authors compute the two-point energy correlator for a high-energy scalar source, using numerical methods to handle the intractable analytic solutions. They find that running coupling induces a decay of the correlator at small angular separations on the celestial sphere, in contrast to the constant, isotropic adS result, while the back-to-back limit exhibits an exponential falloff similar to hard-wall confinement. The introduced parameter $\delta$ smoothly interpolates between RS-like hard-wall confinement ($\delta\to0$) and gauge-theory-like running, offering a framework to study how running and confinement modify energy-flow observables with potential connections to QCD-like phenomenology.

Abstract

We calculate energy correlators in a holographic model incorporating elements of asymptotic freedom and confinement. We model a running coupling by considering a geometry with a warp factor that deviates logarithmically from anti-de Sitter (AdS). A novel aspect of our bulk metric is that it smoothly interpolates between a Randall-Sundrum solution with a hard wall and a geometry corresponding to a logarithmic running typical of gauge theories. By studying shockwave deformations of this metric, we compute a two-point energy correlator assuming a high-energy scalar source. This extends techniques recently developed for correlators in asymptotically AdS geometries. We use numerical methods to find the profile of shockwaves along the extra dimension, as it does not admit an analytical form. The running coupling leads to a decay of the two-point correlator at small angular separation, unlike the flat correlator one finds in AdS. In the back-to-back limit we observe an exponential falloff similar to other hard-wall models.

Figures (2)

• Figure 1: The two-point energy correlator as a function of distance on the transverse plane $r = \lvert x^{\perp} \rvert$ (note the log scale). The burgundy curve corresponds to the model with a running coupling. For comparison we show the correlator for a simple hard wall (RS) model in blue. The normalization is arbitrary. We choose to set the correlators to be equal at a point at large $\lvert x^\perp \rvert$ for visualization purposes. The black dashed line shows a fit of the correlator for the running model to a $1/r^3$ power law.
• Figure 2: The effect of varying the model parameters on the two-point energy correlator. In the left panel we show the correlator for three different locations of the IR brane $v_0 =3, 5, 10$, holding $\delta = 1$ fixed. In the right panel we show the correlator for $\delta^2 = 2, 3/2, 3/5, 3/10$, with a fixed brane location $v_0=5$. We choose the normalization such that the correlator is one at $x^\perp = 0$.