[Paper Review] Collisions in Non-conformal Theories: Hydrodynamization without Equilibration

Maximilian Attems, Jorge Casalderrey-Solana+5 more|arXiv (Cornell University)|Apr 21, 2016

High-Energy Particle Collisions Research1 references3 citations

TL;DR

This paper investigates hydrodynamization in non-conformal strongly coupled field theories using holographic methods, showing that systems can rapidly approach hydrodynamic behavior without reaching thermal equilibrium. The key result is that hydrodynamization occurs earlier than equilibration, even in non-conformal theories, due to the interplay between non-conformal corrections and the dynamics of the dual gravitational background.

ABSTRACT

Maximilian Attems, Jorge Casalderrey-Solana, 2 David Mateos, 3 Daniel Santos-Olivan, Carlos F. Sopuerta, Miquel Triana, and Miguel Zilhao Departament de Fisica Quantica i Astrofisica & Institut de Ciencies del Cosmos (ICC), Universitat de Barcelona, Marti i Franques 1, 08028 Barcelona, Spain Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom Institucio Catalana de Recerca i Estudis Avancats (ICREA), Lluis Companys 23, Barcelona, Spain Institut de Ciencies de l’Espai (CSIC-IEEC), Campus UAB, Carrer de Can Magrans s/n, 08193 Cerdanyola del Valles, Spain

Motivation & Objective

• Understand the dynamics of strongly coupled non-conformal field theories after a high-energy collision.
• Investigate whether hydrodynamization—approach to hydrodynamic behavior—can occur independently of thermal equilibration in non-conformal systems.
• Explore the role of non-conformal corrections in modifying the timescale and nature of hydrodynamization compared to conformal theories.
• Determine if hydrodynamic attractors emerge in non-conformal setups, even when the system remains far from equilibrium.
• Clarify the relationship between hydrodynamization and equilibration in non-conformal holographic models.

Proposed method

• Employ holographic techniques to model non-conformal field theories via a dual gravitational background with a non-trivial dilaton profile.
• Simulate high-energy collisions in the bulk by introducing shockwave initial conditions in the gravitational theory.
• Analyze the time evolution of the stress-energy tensor and its approach to hydrodynamic form using numerical relativity methods.
• Extract hydrodynamic modes and their relaxation times from the late-time behavior of the gravitational solution.
• Compare the timescale of hydrodynamization with that of equilibration by tracking the approach to local equilibrium.
• Use the gradient expansion and late-time analysis to identify the emergence of hydrodynamic attractors in the non-conformal setup.

Experimental results

Research questions

• RQ1 Can hydrodynamization occur in non-conformal field theories without the system reaching thermal equilibrium?
• RQ2 How do non-conformal corrections affect the timescale of hydrodynamization compared to conformal theories?
• RQ3 Do hydrodynamic attractors emerge in non-conformal holographic models, and how do they differ from their conformal counterparts?
• RQ4 What is the relationship between the onset of hydrodynamic behavior and the full equilibration process in non-conformal systems?
• RQ5 How does the presence of a non-trivial dilaton field alter the dynamics of the gravitational background during collisional evolution?

Key findings

• Hydrodynamization occurs significantly earlier than equilibration in non-conformal field theories, indicating that hydrodynamic behavior can emerge before local thermal equilibrium is reached.
• Non-conformal corrections delay the onset of equilibration but do not prevent hydrodynamization, which still occurs on a timescale comparable to that in conformal theories.
• Hydrodynamic attractors are observed in the non-conformal setup, suggesting that hydrodynamic behavior is robust even in the absence of conformal invariance.
• The stress-energy tensor approaches a hydrodynamic form rapidly, with deviations from hydrodynamics decaying exponentially on a timescale set by the non-conformal coupling.
• The late-time behavior of the gravitational solution exhibits universal hydrodynamic scaling, confirming the emergence of a hydrodynamic attractor in the non-conformal context.
• The analysis confirms that the system can exhibit hydrodynamic behavior—characterized by a well-defined fluid velocity and temperature—while still being far from global equilibrium.