Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation

Area of Science:

• * Theoretical physics
• * High-energy nuclear physics
• * Quantum chromodynamics

Background:

• * Relativistic viscous hydrodynamics formulations often suffer from asymptotic, non-convergent gradient expansions due to short-lived modes.
• * The Müller-Israel-Stewart theory provides a framework for describing systems like the quark-gluon plasma.

Purpose of the Study:

• * To identify hydrodynamics as a universal attractor in a longitudinally expanding quark-gluon plasma.
• * To demonstrate that this attractor can be recovered from divergent gradient expansions.
• * To explore the role of short-lived modes and resurgence theory in this recovery.

Main Methods:

• * Application of the Müller-Israel-Stewart theory to a longitudinally expanding quark-gluon plasma.
• * Identification of hydrodynamics as a universal attractor without relying on gradient expansions.
• * Employing Borel summation to recover the attractor from divergent gradient expansions.
• * Analyzing the contribution of short-lived modes and applying resurgence theory.

Main Results:

• * Strong evidence is presented for the existence of a universal hydrodynamic attractor.
• * The divergent gradient expansion is shown to yield the attractor through Borel summation.
• * The importance of accounting for short-lived modes is highlighted, revealing intricate mathematical structures from resurgence theory.

Conclusions:

• * Hydrodynamics acts as a universal attractor in relativistic viscous systems, such as the quark-gluon plasma.
• * Resurgence theory and Borel summation offer a method to reconcile divergent gradient expansions with convergent physical behavior.
• * The study provides a novel mathematical framework for understanding the dynamics of strongly interacting matter.