Welcome

Introductory lecture

• Riccardo Penco

Plenary talk

• Ira Rothstein

Invited talk

• Maria Rodriguez

Invited talk

• Alessandro Podo

Quantum dynamics of perfect fluids

• Petar Tadić (University of Oxford)

We study the quantum field theory of zero-temperature perfect fluids. These systems can be defined by quantizing a classical field theory of scalar fields $\phi^I$, which act as Lagrange coordinates on an internal spatial manifold of fluid configurations. Invariance under volume-preserving diffeomorphisms acting on these scalars implies that the long-wavelength spectrum contains vortex (transverse) modes with an exact $\omega_T=0$ dispersion relation. As a result, physically interpreting the theory within perturbative quantization has proven challenging. In this talk, I will show that correlators evaluated in a class of semi-classical (Gaussian) initial states prepared at $t=0$ are nevertheless well-defined and accessible via perturbation theory. The width of the initial state effectively acts as an infrared regulator, without explicitly breaking the diffeomorphism invariance of the classical action. As an application, I will present the computation of stress-tensor two-point correlators and show that vortex modes give a non-trivial contribution to the response function, which is non-local in both space and time.

eta/s corrections from near-extremal, near-horizon quantum fluctuations

• Clément Supiot (CPHT, École Polytechnique)

Extremal black holes have the particularity of exhibiting an emergent geometry close to their horizon that contains an AdS2 factor. For compact internal spaces, the theory can be dimensionally reduced to obtain a dilaton gravity in two dimensions. At the linearised level, this reduces to JT gravity. The low-energy effective theory is governed by the Schwarzian action, enabling corrections to the entropy and to correlators of the dual near CFT1 to be computed, arising from quantum fluctuations of near-horizon zero modes. By studying shear diffusion, it is in principle possible to compute the effect of these corrections on the ratio viscosity over entropy density, which is conjectured to have a positive lower bound for any fluid. Saturated in numerous holographic systems at the classical gravity level, we address whether such quantum corrections change the picture. Using a matching calculation, we focus on the hydrodynamic regime, for which only weak quantum fluctuations can be considered in order to avoid entering a sub-Planckian regime.

EFT for electrodynamics in general media and Chiral anomalous MHD

• Hong Liu

Invited talk

• Luca Delacretaz

EFT and hydrodynamics far from equilibrium

• Michal Heller

Schwinger-Keldysh hydrodynamics of the SYK lattice

• Akash Jain (University of Amsterdam)

The SYK model and its generalizations provide a rare analytically solvable window into many-body quantum chaos. In this talk, we will study a spatially local generalization of the model, the SYK lattice. We will extend it onto the Schwinger–Keldysh closed-time contour, and perform a long wavelength expansion to arrive at the corresponding local SK EFT. This derivation illustrates how hydrodynamic variables are embedded into the microscopic degrees of freedom, and allows us to compute all transport coefficients for the SYK lattice. Based on arxiv:2604.18675, with Marta Bucca, Mark Mezei and Alexey Milekhin.

Free mutual information and higher-point OTOCs

• Shreya Vardhan (California Institute of Technology)

We introduce a quantity called the free mutual information (FMI), adapted from concepts in free probability theory, as a new physical measure of quantum chaos. This quantity captures the spreading of a time-evolved operator in the space of all possible operators on the Hilbert space, which is doubly exponential in the number of degrees of freedom. It thus provides a finer notion of operator spreading than the well-understood phenomenon of operator growth in physical space. We derive two central results which apply in any physical system: first, an explicit ``Coulomb gas'' formula for the FMI of two observables A(t) and B in terms of the eigenvalues of the product operator A(t)B; and second, a general relation expressing the FMI as a weighted sum of all higher-point out-of-time-ordered correlators (OTOCs). This second result provides a precise information-theoretic interpretation for the higher-point OTOCs as collectively quantifying operator ergodicity and the approach to freeness. This physical interpretation is particularly useful in light of recent progress in experimentally measuring higher-point OTOCs. We identify universal behaviours of the FMI and higher-point OTOCs across a variety of chaotic systems, including random unitary circuits and chaotic spin chains, which indicate that spreading in the doubly exponential operator space is a generic feature of quantum many-body chaos. At the same time, the non-generic behavior of the FMI in various non-chaotic systems, including certain unitary designs, shows that there are cases where an operator spreads in physical space but remains localized in operator space. The FMI is thus a sharper diagnostic of chaos than the standard 4-point OTOC. Based on arXiv:2509.13406.

Amplitudes for Hawking Radiation

• Rafael Aoude (University of Edinburgh)

In this talk, I will present an approach to computing Hawking radiation that is based on on-shell scattering amplitudes. The Hawking spectrum is obtained by exponentiating a series of Feynman diagrams describing the scattering of a massless scalar field through a collapsing background. Using semiclassical methods, we derive a generalisation of an amplitude closely related to the Bogoliubov coefficients. This relates pair production to one-to-one scattering on a background via crossing. Finally, I will replace the background with a coherent-state description of the collapse process and describe it with a purely flat-space approach.

Plenary talk

• Andrew Tolley

Dissipative inflation in the CMB

• Santiago Agui-Salcedo

There is an increasing interest in the interplay between Open Quantum Systems and Inflationary Physics. A time-dependent background and limited access to the degrees of freedom invite the use of Open Quantum systems. It provides a more general framework than the unitary time evolution of a free state. In this talk, based on 2404.15416 and 2507.03103, we develop a local EFT for the scalar curvature perturbations subject to the dynamics of an open quantum system. We recover the scale-invariant power spectrum and then move on to the bispectrum. We study its amplitude and shape as a function of dissipation and other EFT parameters. Our results largely generalise the setup of warm inflation to general non-equilibrium cases. Finally, I will discuss the search for dissipative dynamics in the CMB bispectrum and the current constraints on the dissipation scale.

Invited talk

• Scott Melville

Plenary talk

• Riccardo Rattazzi

Invited talk

• Natalia Pinzani Fokeeva (INFN Firenze)

Invited talk

• Felix Hael

An open EFT for stochastic inflation

• Sebastian Cespedes (Imperial College London)

Understanding stochastic inflation beyond the Gaussian approximation remains an open problem. In this talk I present a framework in which it emerges as the infrared limit of a controlled coarse-graining procedure. First, I construct an open effective field theory for long-wavelength modes from the reduced density matrix. Time locality follows from the thin-shell expansion, while spatial locality emerges in the super-Hubble regime. The resulting Schwinger--Keldysh EFT contains dissipation and diffusion operators, with diffusion dominating in the infrared, yielding the Fokker--Planck equation and systematic corrections. Second, I reinterpret coarse-graining as an RG flow for the density matrix. Stochastic dynamics arises after taking the super-Hubble and gradient-expansion limits. The flow obeys a Polchinski-type equation, which generates the EFT structure and leads to a generalised Fokker--Planck equation capturing subleading corrections.

Non-equilibrium particle production in the early universe

• Matthias Carosi

The out-of-equilibrium evolution of the early universe plays a central role in addressing some of the most pressing outstanding puzzles of particle physics, such as the matter-antimatter asymmetry and the production of dark matter. A consistent description of the non-equilibrium dynamic of the system requires systematically incorporating quantum and thermal effects, which can be achieved via the Schwinger-Keldysh formalism together with the two-particle-irreducible (2PI) effective action. In this talk, I show how this first-principle approach can be used to study particle production during non-equilibrium stages of the early-universe evolution. In particular, I demonstrate how the same framework captures both perturbative particle production, governed by scattering processes, and non-perturbative production arising from non-adiabatic, coherent dynamics. I illustrate this in two phenomenologically relevant settings: the real-time dynamics of bubbles in first-order phase transitions, and the preheating epoch following inflation.

Dissipative EFTs in cosmology

• Perseas Christodoulidis (Ewha Womans Universtity)

We construct a gravitational open extension of the effective field theory of inflation in the Schwinger-Keldysh framework. While physical symmetries allow many open operators in the Schwinger-Keldysh action, most of them overconstrain the equations of motion, yielding inconsistent dynamics. We identify the minimal open operators compatible with propagating scalar and tensor modes and build the gravitational action, recovering dissipative models of inflation.

Effective action for dissipative fluids from Schwinger-Keldysh holography

• Inna Ivanova (Ben-Gurion University of the Negev (BGU))

We derive the all-order effective action for a dissipative neutral relativistic fluid using a holographic Schwinger-Keldysh closed-time-path formalism, where the dual gravitational theory is Einstein gravity in an asymptotically AdS spacetime. The effective action is obtained by solving the double Dirichlet problem for linearized gravitational perturbations on a complexified asymptotically AdS geometry within the saddle-point approximation. The resulting boundary effective action, computed to quadratic order in AdS boundary data and to all orders in the derivative expansion, simultaneously captures both fluctuation and dissipation within a single covariant framework.

The discovery of hot water: the Schwinger-Keldysh coset construction for dissipative fluids and superfluids at finite temperature

• Paolo Arcangeli (TUM)

Recent developments in the Schwinger–Keldysh (SK) formalism have enabled significant progress in the construction of effective field theories (EFTs) for out-of-equilibrium systems at finite temperature. Nevertheless, existing results in the literature lack a systematic and transparent framework for deriving SK EFT actions for generic fluid systems. In this talk, I will apply the coset construction method – adapted for possible breaking of spacetime symmetries – to derive SK EFT Lagrangians at first dissipative order, which describe generic fluid systems. These are systems whose ground state spontaneously breaks spacetime symmetries in a way characteristic of fluids, without imposing any specific assumption on the internal symmetry content. Focusing on $U(1)$-charged fluids and superfluids as concrete examples, I will derive phenomenological consequences, including local equilibrium thermodynamic relations, the entropy current and the local second law of thermodynamics, and dissipative dispersion relations. All results are consistent with previously known outcomes in the literature, thereby reinforcing the validity and potential of the approach.

Stability analysis of first order hydrodynamics as IR effective theory

• Atsuhisa Ota (Chongqing University)

In this talk we discuss the mode structure of general U(1)-charged first-order relativistic hydrodynamics, formulated within an effective field theory for dissipative fluids in flat Minkowski spacetime. Although first-order relativistic hydrodynamics is known to be ill-posed as a system of partial differential equations, we argue that this conclusion is potentially misleading because hydrodynamics is not a fundamental theory. We derive the most general quadratic action for hydrodynamic modes, including stochastic noise, and analyze the resulting dispersion relations within a controlled gradient expansion. We then show that frame-invariant combinations of hydrodynamic transport coefficients fix the first-order dispersion relations in the low-energy limit, making the mode analysis manifestly independent of the choice of hydrodynamic frame. Assuming local Kubo-Martin-Schwinger (KMS) symmetry and unitarity of the underlying UV theory, we find that first-order hydrodynamics is stable provided the enthalpy density is positive.

Phases and Symmetry Breaking in the Dissipative SYK Model via the Keldysh Formalism

• Amaury Jean (University of Cambridge)

The dissipative Sachdev-Ye-Kitaev (SYK) model has recently emerged as a paradigmatic toy model of strongly interacting open quantum systems coupled to a Markovian bath, whose dynamics is governed by a Lindblad master equation. The Keldysh double-contour technique allows for analytical progress in the limit of a large number of fermion flavours, by mapping the path integral of the open SYK model to that of two coupled non-Hermitian SYK systems, where thermal phase transitions between black hole and wormhole phases have been identified. While dynamical phase transitions between such phases were previously studied, a systematic investigation of the possible phases and their symmetry properties remained unexplored. Here, we address this problem by solving the Schwinger–Dyson equations derived from the Keldysh path integral across all possible symmetry sectors, thus clarifying the nature of these phases and the patterns of symmetry breaking that underpin relaxation dynamics.

A holographic prescription for dissipative hydrodynamical actions and horizon symmetries

• Mike Blake (University of Bristol)

The last decade has seen significant interest in dissipative hydrodynamical actions in the Schwinger-Keldysh formalism. However there remain very few examples where such actions can be explicitly constructed. I will present a novel prescription that allows, for the first time, one to consistently compute such actions for holographic quantum field theories in general bulk dimension. The explicit construction of such actions allows us to test conjectured relations between hydrodynamical actions and quantum chaos – in particular I will discuss to what extent such actions realise horizon symmetries previously argued for by Knysh, Liu & Pinzani-Fokeeva.

From effective field theory of fluids with higher-form symmetries to kinetic theory of strings

• Saso Grozdanov

Open Quantum Systems for Cosmological Observers

• Omkar Shetye (Instytut Fizyki Teoretycznej, Uniwersytet Jagielloński)

Inspired by similar constructions for AdS blackholes, we propose a geometric method that computes the Schwinger-Keldysh effective action describing the dynamics of a localised observer in de Sitter spacetime. This action describes the dissipative physics of radiation reaction of the observer as well as the Hawking radiation seen by it. Our geometric construction implicitly encodes the fluctuation-dissipation theorem at a non-linear level. We perform various checks on our computation matching the flat space limit to previous calculations and verifying the consistency with symmetry arguments.

Self-consistent computation of pair production from non-relativistic effective field theories in the Keldysh-Schwinger formalism

• Tobias Binder (TUM)

Sommerfeld-enhanced annihilation cross sections in the presence of nearly zero-energy bound states can become so large that perturbative partial-wave unitarity appears to be violated. Previous literature incorporated the short-distance annihilation potential self-consistently into the computation of the Schrödinger wave function at the origin, leading to the unitarization of the Sommerfeld effect in vacuum. We employ non-relativistic effective field theory methods and the Keldysh-Schwinger formalism to additionally include pair-creation effects in the self-consistent computation of four-point correlation functions, which renders the unitarization temperature dependent. Up to small thermal corrections in the non-relativistic and dilute regime of the pairs, we confirm the previous results based on the Schrödinger equation approach for scattering states in vacuum. For the first time, we analyze bound-state contributions beyond their leading decay via annihilation. Interestingly, our self-consistent computation of the four-point correlation function shows that bound states remain on-shell in their out-of-equilibrium decay, even though their spectral functions take the form of Breit–Wigner distributions due to finite decay widths. While this may appear paradoxical, it aligns with expectations from earlier results based on exact analytic solutions of the Kadanoff–Baym equations for a decaying elementary particle in a thermal environment.

Real-Time Nucleation in High-Temperature Quantum Field Theories

• Joonas Hirvonen (University of Nottingham)

In this talk, we study thermal nucleation in quantum field theories in real time. We begin by discussing an effective description of the real-time plasma emerging from the Schwinger–Keldysh formalism. This description consists of a Boltzmann equation for out-of-equilibrium particles and a classical field equation for a fluctuating scalar field responsible for nucleation. We show that, at the order considered in perturbation theory, the scalar potential coincides with the corresponding equilibrium effective potential. Applying classical nucleation theory to this framework yields a nucleation rate formula. Our results corroborate the standard equilibrium predictions up to a certain level of accuracy, while also incorporating real-time corrections. We also identify an infrared divergence associated with out-of-equilibrium bosonic contributions, highlighting an important direction for future work.