Universal properties of Chaos and Hydrodynamics

Project Information

UniCHydro

Grant agreement ID: 886540

DOI

10.3030/886540

Project closed

EC signature date 17 April 2020

Start date 1 February 2021

End date 25 May 2025

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 269 002,56

EU contribution

€ 269 002,56

Coordinated by

UNIVERSITA DEGLI STUDI DI FIRENZE
Italy

Periodic Reporting for period 2 - UniCHydro (Universal properties of Chaos and Hydrodynamics)

Reporting period: 2023-02-01 to 2024-01-31

Summary of the context and overall objectives of the project

Fluid dynamics is a well-established field with roots going back to Archimedes. Yet, its theoretical foundations continue to evolve, especially as new challenges and perspectives emerge. In recent years, modern techniques from theoretical physics have led to a reformulation of fluid dynamics from first principles, moving beyond traditional approaches that relied primarily on empirical observations. Crucially, this new framework enables the systematic inclusion of stochastic thermal fluctuations—tiny, random variations in the medium that can significantly influence the large-scale properties of the fluid, such as its viscosity. Understanding these effects is essential for accurately describing complex systems, particularly near phase transitions and in turbulent flows.

A striking real-world application appears in high-energy heavy-ion collisions at CERN’s Large Hadron Collider. In these extreme events, quarks and gluons are liberated from their parent nuclei and form a hot, dense, and strongly interacting fluid known as the quark-gluon plasma. As the plasma expands and cools, the quarks and gluons recombine into hadrons. Depending on the system’s energy and conserved charges, this recombination can happen smoothly or via a first-order phase transition, much like the freezing of water into ice. This behavior suggests the possible existence of a critical point—a special region in the QCD phase diagram where the smooth and abrupt transitions meet, and where fluctuations play a significant role. Locating this critical point is a major goal of current experimental and theoretical research.

This project has two main objectives. First, it aims to construct explicit scenarios where the new formulation of fluid dynamics can be applied—for example, in spin hydrodynamics, to study globally rotating plasmas. These spinning fluids naturally arise in non-central heavy-ion collisions, where the fluid’s internal spin and rotational motion become important and interact in subtle ways. The project also aims to develop a comprehensive framework for describing the physics near the QCD critical point using this modern fluid dynamics approach, thereby contributing directly to ongoing efforts to experimentally discover the critical point

The second goal is to explore deep and surprising connections between this reformulated fluid dynamics and the physics of black holes. In theoretical physics, black holes are not just astrophysical objects but also powerful tools for probing ideas in quantum gravity. Remarkably, black holes behave like thermodynamic systems—they have temperature and entropy—and, in certain contexts, they even exhibit fluid-like behavior near their horizons. This is especially apparent in the framework of the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, which links a gravitational theory in a higher-dimensional space to a quantum field theory without gravity in lower dimensions.

This project has made significant progress in applying the new formulation of fluid dynamics to physical systems relevant to heavy-ion phenomenology, while also uncovering deep connections between the symmetries of black hole horizons and those of hydrodynamic and chaotic systems. These results not only advance our theoretical understanding but also open new avenues for exploring the interplay between quantum gravity, fluid dynamics, and many-body quantum physics.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Together with a team at the University of Amsterdam, I developed novel techniques to compute the effective field theory of fluid dynamics from first principles using holography—a framework that relates theories of gravity to certain quantum field theories in one higher dimension. Beyond deriving the effective field theory for the simplest case of charge diffusion, we made significant progress in computing the effective theory for linearized fluid dynamics and chaotic systems, including advances toward an effective action for chaos.

In collaboration with researchers at KU Leuven, Belgium, I applied new methods to analyze the information content of Hawking radiation within a simplified two-dimensional multiverse model. Our published work offered fresh insights into how holographic information might be encoded in spacetimes with a positive cosmological constant.

Working with a team at Technion, Israel, I constructed a new conserved current in both relativistic and nonrelativistic hydrodynamics in 2+1 dimensions. To support these results, I derived this current as a Noether current from an effective field theory formulation of fluid dynamics. Crucially, I identified the corresponding horizon symmetry of 3+1-dimensional Anti-de Sitter black holes that is dual to the symmetry responsible for enstrophy conservation in fluids. These findings were published across three papers, including one in the prestigious Physical Review Letters.

Collaborating with teams at MIT and VUB Brussels, I conducted original research enabling a novel interpretation of black hole horizon symmetries.

At the University of Florence, I organized a major five-week workshop bridging heavy-ion collision phenomenology, experiments, and theoretical physics—Foundations and Applications of Relativistic Hydrodynamics—held at the Galileo Galilei Institute. The event, hosting about 40 participants per week, was highly successful and received positive feedback.

Finally, alongside researchers at the University of Florence, I contributed to developing a consistent theory of rotating and spinning plasma, as well as a first-principles effective theory of the QCD critical point.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Upon derivation of an effective field theory for linearized fluid dynamics and chaotic systems, it will be possible to set on solid grounds the new formulation of fluid dynamics. Moreover, new entries to the holographic dictionary will be provided in such a way that our results can be potentially used for other holographic derivations of effective field theories beyond the simple vanilla fluid dynamics, such as superfluid, etc.

Having established the black hole horizon symmetry responsible for enstrophy conservation in asymptotically 3+1 dimensional Anti-de Sitter spacetimes, with the team in Israel we are currently working on the possibility of establishing the existence of enstrophy conservation in general 3+1 dimensional spacetimes, not necessarily Anti-de Sitter. In this way, it will be possible to go beyond the holographic correspondence and define a symmetry principle on the same footing as entropy conservation in black hole mechanics.

Our result on black hole horizon symmetries and the connection to hydrodynamics and chaos led to a new prediction. We expect to test this prediction and to study the effects of this new symmetry constraint on the correlation functions of an effective field theory for chaotic systems before the end of this project.

Also, with the team at the University of Florence, I am applying the effective field theory techniques for fluid dynamics to the phenomenology of heavy ion collisions. In particular to the problem of searches of the critical point in the phase space of quantum chromodynamics and to the problem of global polarization and hydrodynamics with spin in the quark gluon plasma.

The Schwinger-Keldysh effective field theory spaces