arXiv subjects

Ludovic Varrin

Publications and source records attributed to Ludovic Varrin.

12 recordsLinked to original sources

arXiv2026

Quantum Geometry from Area Fluctuations

We construct a quantum-statistical analogue of Einstein's fluctuation argument for black-body radiation in the context of causal-diamond geometry. Starting from the phase space of a stretched horizon inside a Minkowski causal diamond, we quantize the Poisson algebra generated by the fields averaged over stretched-horizon time. We then compute the fluctuations of the averaged area density of the transverse two-spheres in a thermal state constructed in analogue with the black-body thermal state. In the null limit, where the stretched horizon approaches the causal-diamond boundary, this yields a thermal fluctuation formula of the boundary area operator that contains two terms, in direct analogue with the black-body radiation. The term quadratic in the expectation value is the ``classical'' contribution, while the linear term has the Verlinde--Zurek scaling characteristic of independent microscopic constituents. In direct analogue with Einstein's interpretation of black-body energy fluctuations as evidence for light quanta, we interpret the linear area-fluctuation term as a statistical signature of discrete quanta of geometry. This provides bottom-up evidence for quantum area degrees of freedom and supports the embadon picture of null quantum geometry.

hep-th↗

arXiv2026

At the Corner of Quantum and Gravity

In the presence of spacetime boundaries, diffeomorphisms in gravitational theories can become physical and acquire non-vanishing Noether charges. These charges obey an algebra which, within the extended phase-space formalism, faithfully realizes diffeomorphism algebra. The corner proposal takes this algebra of physical corner symmetries as a fundamental ingredient of quantum gravity, in close analogy with the role of the Poincar\'e group in quantum field theory. In this thesis we develop the quantum corner framework in the two-dimensional setting. We give the full representation theory of the two-dimensional extended corner symmetry group, which may be interpreted either as the symmetry group of two-dimensional gravity or as the corner symmetry group relevant for four-dimensional spherically symmetric gravity. Within the corner proposal, the resulting representation spaces are then interpreted as candidate Hilbert spaces for quantum gravity. This representation-theoretic structure naturally enables a description of local subsystems. In particular, we present a gluing procedure that constructs quantum states associated with an entangling corner between two spacetime subregions, and use it to compute the entanglement entropy between the two regions. To connect the quantum observables to the classical corner charges, we construct the coadjoint orbits of the quantum corner symmetry group and relate them to the classical structure through twisted moment maps and to the quantum structure through generalized Perelomov coherent states. This provides a notion of semiclassical limit within the corner framework. Finally, in the context of static, spherically symmetric spacetimes, we show that a distinguished family of coherent states reproduces the horizon area law for entropy in the semiclassical limit, yielding a quantum, symmetry-based explanation of the Bekenstein--Hawking formula.

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arXiv2026

On the non-commutativity of geometric observables in different Lorentz frames

Our aim is to establish whether geometric observables, such as length, area or volume of a physical object, viewed by different observers Poisson commute or not. To illustrate this, we compute the Poisson bracket of two lengths associated to a rigid rod and measured by two different geodesic (inertial) observers, one of which is at rest while the other is moving with respect to the rod. Our calculation shows that geometric observables measured by different observers generically do not Poisson commute, not even in Minkowski spacetime. This non-trivial result provides interesting insights into questions related to the presence of a fundamental scale in the context of quantum gravity.

gr-qc↗

arXiv2025

From the Corner Proposal to the Area Law

We provide an explicit realization of the Corner Proposal for Quantum Gravity in the case of spherically symmetric spacetimes in four dimensions, or equivalently, two-dimensional dilaton gravity. We construct coherent states of the Quantum Corner Symmetry group and compute the entanglement entropy relative to these states. We derive the classical corner charges and relate them to operator expectation values in coherent states. For a subset of coherent states that we call classical states, we find that the entanglement entropy exhibits a leading term proportional to the area, recovering the Bekenstein-Hawking area law in the semiclassical limit.

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arXiv2025

Semi-Classical Limit of Quantum Gravity on Corners

We study quantum and classical systems associated with the quantum corner symmetry group $\mathrm{QCS}=\widetilde{\mathrm{SL}}(2,\mathbb{R})\ltimes \mathrm{H}_3,$ which arises in the context of quantum gravity. We relate quantum observables -- specified by representation-theoretic data -- to their classical counterparts using generalized Perelomov coherent states and the framework of Berezin quantization. This procedure links abstract representation-theoretic input to geometric classical observables, such as area. We conclude by applying the formalism to static, spherically symmetric spacetimes admitting a horizon.

hep-th↗

arXiv2025

Entanglement Entropy of Quantum Corners

In gravitational theories with boundaries, diffeomorphisms can become physical and acquire a non-vanishing Noether charge. Using the covariant phase space formalism, on shell of the gravitational constraints, the latter localizes on codimension-$2$ surfaces, the corners. The corner proposal asserts that these charges, and their algebras, must be important ingredients of any quantum gravity theory. In this manuscript, we continue the study of quantum corner symmetries and algebras by computing the entanglement entropy and quantum informational properties of quantum states abiding to the quantum representations of corners in the framework of $2$-dimensional gravity. We do so for two classes of states: the vacuum and coherent states, properly defined. We then apply our results to JT gravity, seen as the dimensional reduction of $4$d near extremal black holes. There, we demonstrate that the entanglement entropy of some coherent quantum gravity states -- states admitting a semiclassical description -- scales like the dilaton, reproducing the semiclassical area law behavior and further solidifying the quantum informational nature of entropy of quantum corners. We then study general states and their gluing procedure, finding a formula for the entanglement entropy based entirely on the representation theory of $2$d quantum corners.

hep-th↗

arXiv2025

Orbit method for Quantum Corner Symmetries

The classification of the unitary irreducible representations of symmetry groups is a cornerstone of modern quantum physics, as it provides the fundamental building blocks for constructing the Hilbert spaces of theories admitting these symmetries. In the context of gravitational theories, several arguments point towards the existence of a universal symmetry group associated with corners, whose structure is the same for every diffeomorphism-invariant theory in any dimension. Recently, the representations of the maximal central extension of this group in the two-dimensional case have been classified using purely algebraic techniques. In this work, we present a complementary and independent derivation based on Kirillov's orbit method. We study the coadjoint orbits of the group $\widetilde{\mathrm{SL}}(2,\mathbb{R})\ltimes\mathbb{H}_3$, where $\mathbb{H}_3$ is the Heisenberg group of a quantum particle in one dimension. Our main result is that, despite the non-abelian nature of the normal subgroup in the semidirect product, these orbits admit a simple description. In a coordinate system associated with modified Lie algebra generators, the orbits factorize into a product of coadjoint orbits of $\mathrm{SL}\left(2,\mathbb{R}\right)$ and $\mathbb{H}_3$. The subsequent geometric quantization of these factorized orbits successfully reproduces the known representations.

hep-th↗

arXiv2024

Physical Representations of Corner Symmetries

We give the full representation theory of the gravitational extended corner symmetry group in two-dimensions. This includes projective representations, which correspond to representations of the quantum corner symmetry group. We find that they are described by one-dimensional conformal fields with an additional index in the Fock space of the harmonic oscillator. We begin with a review of Mackey's theory of induced representations and then proceed to its application to the corner symmetries. The field representations, induced from the irreducible representations of the special linear group are worked out first. The little group method is then applied to the extended corner symmetry group to obtain the irreducible unitary representations. Finally, we focus on projective representations and their application to the description of local subsystems.

hep-th↗

arXiv2024

Quantum Corner Symmetry: Representations and Gluing

The corner symmetry algebra organises the physical charges induced by gravity on codimension-$2$ corners of a manifold. In this letter, we initiate a study of the quantum properties of this group using as a toy model the corner symmetry group of two-dimensional gravity $\mathrm{SL}\left(2,\mathbb{R}\right)\ltimes \mathbb{R}^2$. We first describe the central extensions and how the quantum corner symmetry group arises and give the Casimirs. We then make use of one particular representation to discuss the gluing of corners, achieved by identifying the maximal commuting sub-algebra. This is a concrete implementation of the gravitational constraints at the quantum level.

hep-th↗

arXiv2023

On the covariant formulation of gauge theories with boundaries

In the present article, we review the classical covariant formulation of Yang-Mills theory and general relativity in the presence of spacetime boundaries, focusing mainly on the derivation of the presymplectic forms and their properties. We further revisit the introduction of the edge modes and the conditions which justify them, in the context where only field-independent gauge transformations are considered. We particularly show that the presence of edge modes is not justified by gauge invariance of the presymplectic form, but rather by the condition that the presymplectic form is degenerate on the initial field space, which allows to relate this presymplectic form to the symplectic form on the gauge reduced field space via pullback.

hep-th↗

arXiv2023

Consistent first order action functional for gauge theories

A novel first order action principle has been proposed as the possible foundation for a more fundamental theory of General Relativity and the Standard Model. It is shown in this article that the proposal consistently incorporates gravity and matter fields, and guides to a new and robust path towards unification of fundamental interactions.

hep-th↗

arXiv2023

Cornering Quantum Gravity

After introducing the covariant phase space calculus, Noether's theorems are discussed, with particular emphasis on Noether's second theorem and the role of gauge symmetries. This is followed by the enunciation of the theory of asymptotic symmetries, and later its application to gravity. Specifically, we review how the BMS group arises as the asymptotic symmetry group of gravity at null infinity. Symmetries are so powerful and constraining that memory effects and soft theorems can be derived from them. The lectures end with more recent developments in the field: the corner proposal as a unified paradigm for symmetries in gravity, the extended phase space as a resolution to the problem of charge integrability, and eventually the implications of the corner proposal on quantum gravity.

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