How Gubser flow ends in a holographic conformal theory

TL;DR

This paper investigates the late-time behavior of Gubser flow in holographic conformal field theories, revealing a specific pressure-energy relation and detailed asymptotic properties of the energy-momentum tensor.

Contribution

It provides a detailed analysis of the asymptotic behavior of Gubser flow in holographic CFTs, including the late-time energy-momentum tensor and decay rates of energy density.

Findings

At late de-Sitter time, the plasma reaches a state with = P_T = - P_L.

The energy density decays faster than any power law at large transverse distance.

Energy density vanishes faster than any power as early proper time.

Abstract

Gubser flow is an axis-symmetric and boost-invariant evolution in a relativistic quantum field theory which is best studied by mapping $\mathbf{R}^{3,1}$ to $dS_{3}\times \mathbf{R}$ when the field theory has conformal symmetry. We show that at late de-Sitter time, which corresponds to large proper time and central region of the future wedge within $\mathbf{R}^{3,1}$, the holographic conformal field theory plasma can reach a state in which $\varepsilon = P_T = - P_L$, with $\varepsilon$, $P_T$ and $P_L$ being the energy density, transverse and longitudinal pressures, respectively. We further determine the full sub-leading behaviour of the energy-momentum tensor at late time. Restricting to flows in which the energy density decays at large transverse distance from the central axis in $\mathbf{R}^{3,1}$, we show that this decay should be faster than any power law. Furthermore, in this case the energy density also vanishes in $\mathbf{R}^{3,1}$ faster than any power as we go back to early proper time. Hydrodynamic behavior can appear in intermediate time.