Universal behaviour, transients and attractors in supersymmetric Yang–Mills plasma

Abstract

Numerical simulations of expanding plasma based on the AdS/CFT correspondence as well as kinetic theory and hydrodynamic models strongly suggest that some observables exhibit universal behaviour even when the system is not close to local equilibrium. This leading behaviour is expected to be corrected by transient, exponentially decaying contributions which carry information about the initial state. Focusing on late times, when the system is already in the hydrodynamic regime, we analyse numerical solutions describing expanding plasma of strongly coupled N = 4 supersymmetric Yang-Mills theory and identify these transient effects, matching them in a quantitative way to leading transseries corrections corresponding to least-damped quasinormal modes of AdS black branes. In the process we offer additional evidence supporting the recent identification of the Borel sum of the hydrodynamic gradient expansion with the far-from-equilibrium attractor in this system.

The large proper-time expansion of Yang-Mills plasma as a resurgent transseries

“…Thus, the transseries for the energy density has a similar interpretation as the transseries for quantities which are universal in the sense of Ref. [63] -it describes the dissipation of initial state information in the process of hydrodynamization [9,19,63,64].…”

Holographic Bjorken flow at large-D

“…In this subsection we explore the connection between these two types of non-perturbative contributions. We start by performing the gradient trans-series analyses at arbitrary D. Following [34,35,[58][59][60], at sufficiently late times we can supplement the gradient expansion of the different metric functions (3.36)-(3.38) with non-perturbative (in gradients) contributions in the form of a trans-series…”

Early- and Late-Time Behavior of Attractors in Heavy-Ion Collisions

“…Rather, information about the initial condition is lost only at times t ∼ 1, and only on that timescale solutions converge to a common attractor. By closer inspection of these results (data not shown) we observe that both for early initializations t 0 < 1 and for late initializations t 0 > 1, differences between solutions show the oscillatory behavior characteristic for the decay of quasinormal modes (QNM) [16] that are exponentially damped with timescale τ QNM . These solutions reach a unique attractor only at late times t > 1.…”

“…Recently, such attractors have received attention in the context of ultrarelativistic heavy-ion collisions. Their form is of interest for understanding the onset of fluid-dynamic behavior [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and the origin of the nonthermal fixed-point behavior in far-from-equilibrium dynamics [1,19,[22][23][24][25]. For the phenomenology of heavy-ion collisions, these studies are needed to clarify to what extent different observables inform us either about the details of the initial conditions or about the material properties of the system.…”