Publications (51)
Most general theory of 3d gravity: Covariant phase space, dual diffeomorphisms, and more
Marc Geiller, Christophe Goeller, Nelson Merino
We show that the phase space of three-dimensional gravity contains two layers of dualities: between diffeomorphisms and a notion of "dual diffeomorphisms" on the one hand, and betw…
New Hamiltonians for loop quantum cosmology with arbitrary spin representations
Jibril Ben Achour, Suddhasattwa Brahma, Marc Geiller
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systemati…
Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory
Jorrit Bosma, Marc Geiller, Sucheta Majumdar +1
We study the null asymptotic structure of Einstein-Maxwell theory in three-dimensional (3D) spacetimes. Although devoid of bulk gravitational degrees of freedom, the system admits…
Lorentz-diffeomorphism edge modes in 3d gravity
Marc Geiller
The proper definition of subsystems in gauge theory and gravity requires an extension of the local phase space by including edge mode fields. Their role is on the one hand to resto…
3d gravity in Bondi-Weyl gauge: charges, corners, and integrability
Marc Geiller, Christophe Goeller, Céline Zwikel
We introduce a new gauge and solution space for three-dimensional gravity. As its name Bondi-Weyl suggests, it leads to non-trivial Weyl charges, and uses Bondi-like coordinates to…
Modular polymer representations of the Weyl algebra
Yigit Yargic, Marc Geiller
One of the key conceptual challenges in quantum gravity is to understand how quantum theory should modify the very notion of spacetime. One way to investigate this question is to s…
BTZ Black Hole Entropy and the Turaev-Viro model
Marc Geiller, Karim Noui
We show the explicit agreement between the derivation of the Bekenstein-Hawking entropy of a Euclidean BTZ black hole from the point of view of spin foam models and canonical quant…
Near-Horizon Radiation and Self-Dual Loop Quantum Gravity
Marc Geiller, Karim Noui
We compute the near-horizon radiation of quantum black holes in the context of self-dual loop quantum gravity. For this, we first use the unitary spinor basis of $\text{SL}(2,\math…
Symmetries of the gravitational scattering in the absence of peeling
Marc Geiller, Alok Laddha, Céline Zwikel
The symmetries of the gravitational scattering are intimately tied to the symmetries which preserve asymptotic flatness at null infinity. In Penrose's definition of asymptotic flat…
Quantum dynamics of the black hole interior in LQC
Francesco Sartini, Marc Geiller
It has been suggested that the homogeneous black hole interior spacetime, when quantized following the techniques of loop quantum cosmology, has a resolved singularity replaced by…
Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs
Marc Geiller, Florian Girelli, Christophe Goeller +1
We present a Sugawara-type construction for boundary charges in 4d BF theory and in a general family of related TQFTs. Starting from the underlying current Lie algebra of boundary…
Spin Foams and Canonical Quantization
Sergei Alexandrov, Marc Geiller, Karim Noui
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional…
Electromagnetic duality and central charge from first order formulation
Marc Geiller, Puttarak Jai-akson, Abdulmajid Osumanu +1
In the context of the infrared triangle there have been recent discussions on the existence and the role of dual charges. We present a new viewpoint on dual magnetic charges in …
Celestial charges and the subleading structure of asymptotically-flat spacetimes
Marc Geiller
We study the subleading structure of asymptotically-flat spacetimes and its relationship to the loop algebra of higher spin charges. We do so using both the Bondi-Sa…
Regularized Black Holes from Doubled FLRW Cosmologies
Marc Geiller, Etera R. Livine, Francesco Sartini
Reduced general relativity for four-dimensional spherically-symmetric stationary space-times, more simply called the black hole mini-superspace, was shown in previous work to admit…
Edge modes of gravity. Part III. Corner simplicity constraints
Laurent Freidel, Marc Geiller, Daniele Pranzetti
In the tetrad formulation of gravity, the so-called simplicity constraints play a central role. They appear in the Hamiltonian analysis of the theory, and in the Lagrangian path in…
Minimal massive supergravity and new theories of massive gravity
Nihat Sadik Deger, Marc Geiller, Jan Rosseel +1
We present an action for minimal massive gravity (MMG) in three dimensions in terms of a dreibein and an independent spin connection. Furthermore, the construction provides an acti…
Flux formulation of loop quantum gravity: Classical framework
Bianca Dittrich, Marc Geiller
We recently introduced a new representation for loop quantum gravity, which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the p…
A remarkably simple theory of 3d massive gravity
Marc Geiller, Karim Noui
We propose and study a new action for three-dimensional massive gravity. This action takes a very simple form when written in terms of connection and triad variables, but the conne…
Edge modes of gravity -- II: Corner metric and Lorentz charges
Laurent Freidel, Marc Geiller, Daniele Pranzetti
In this second paper of the series we continue to spell out a new program for quantum gravity, grounded in the notion of corner symmetry algebra and its representations. Here we fo…
Black Hole Entropy from complex Ashtekar variables
Ernesto Frodden, Marc Geiller, Karim Noui +1
In loop quantum gravity, the number of microstates of a black hole for a given discrete geometry depends on the so-called Barbero-Immirzi parameter . Using a…
A note on the Holst action, the time gauge, and the Barbero-Immirzi parameter
Marc Geiller, Karim Noui
In this note, we review the canonical analysis of the Holst action in the time gauge, with a special emphasis on the Hamiltonian equations of motion and the fixation of the Lagrang…
Symmetries of the Black Hole Interior and Singularity Regularization
Marc Geiller, Etera R. Livine, Francesco Sartini
We reveal an Poincaré algebra of conserved charges associated with the dynamics of the interior of black holes. The action of these Noether charges integrate…
A new look at Lorentz-Covariant Loop Quantum Gravity
Marc Geiller, Marc Lachieze-Rey, Karim Noui
In this work, we study the classical and quantum properties of the unique commutative Lorentz-covariant connection for loop quantum gravity. This connection has been found after so…
Dual diffeomorphisms and finite distance asymptotic symmetries in 3d gravity
Marc Geiller, Christophe Goeller
We study the finite distance boundary symmetry current algebra of the most general first order theory of 3d gravity. We show that the space of quadratic generators contains diffeom…
Statistical Entropy of a BTZ Black Hole from Loop Quantum Gravity
Ernesto Frodden, Marc Geiller, Karim Noui +1
We compute the statistical entropy of a BTZ black hole in the context of three-dimensional Euclidean loop quantum gravity with a cosmological constant . As in the four-dimensio…
Quantum gravity kinematics from extended TQFTs
Bianca Dittrich, Marc Geiller
We show how extended topological quantum field theories (TQFTs) can be used to obtain a kinematical setup for quantum gravity, i.e. a kinematical Hilbert space together with a repr…
Spectra of geometric operators in three-dimensional LQG: From discrete to continuous
Jibril Ben Achour, Marc Geiller, Karim Noui +1
We study and compare the spectra of geometric operators (length and area) in the quantum kinematics of two formulations of three-dimensional Lorentzian loop quantum gravity. In the…
Edge modes of gravity -- I: Corner potentials and charges
Laurent Freidel, Marc Geiller, Daniele Pranzetti
This is the first paper in a series devoted to understanding the classical and quantum nature of edge modes and symmetries in gravitational systems. The goal of this analysis is to…
Field-dependent diffeomorphisms and the transformation of surface charges between gauges
Luca Ciambelli, Marc Geiller
When studying gauge theories in the presence of boundaries, local symmetry transformations are typically classified as gauge or physical depending on whether the associated charges…
Minimal Massive Supergravity
Nihat Sadik Deger, Marc Geiller, Jan Rosseel +1
Minimal massive gravity in three dimensions propagates a single massive spin-2 mode around an AdS vacuum. It is distinguished by allowing for vacua with positive central charges of…
BMS Mechanics and the Black Hole Interior
Marc Geiller, Etera R. Livine, Francesco Sartini
The spacetime in the interior of a black hole can be described by an homogeneous line element, for which the Einstein--Hilbert action reduces to a one-dimensional mechanical model.…
The partial Bondi gauge: Further enlarging the asymptotic structure of gravity
Marc Geiller, Céline Zwikel
We present a detailed analysis of gravity in a partial Bondi gauge, where only the three conditions are fixed. We relax in particular the so-called determinant co…
A new vacuum for Loop Quantum Gravity
Bianca Dittrich, Marc Geiller
We construct a new vacuum for loop quantum gravity, which is dual to the Ashtekar-Lewandowski vacuum. Because it is based on BF theory, this new vacuum is physical for -dime…
Black holes as gases of punctures with a chemical potential: Bose-Einstein condensation and logarithmic corrections to the entropy
Olivier Asin, Jibril Ben Achour, Marc Geiller +2
We study the thermodynamical properties of black holes when described as gases of indistinguishable punctures with a chemical potential. In this picture, which arises from loop qua…
Twisting asymptotically-flat spacetimes
Marc Geiller, Pujian Mao, Antoine Vincenti
We extend the Bondi formalism to describe asymptotically-flat spacetimes where the outgoing null geodesic congruence is not hypersurface-orthogonal, i.e. has non-vanishing twist. I…
Hawking radiation by spherically-symmetric static black holes for all spins: II -- Numerical emission rates, analytical limits and new constraints
Alexandre Arbey, Jérémy Auffinger, Marc Geiller +2
In the companion paper [Phys. Rev. D 103 (2021) 10, [2101.02951]] we have derived the short-ranged potentials for the Teukolsky equations for massless spins in genera…
Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity
Marc Geiller
Boundaries in gauge field theories are known to be the locus of a wealth of interesting phenomena, as illustrated for example by the holographic principle or by the AdS/CFT and bul…
Testing the role of the Barbero-Immirzi parameter and the choice of connection in Loop Quantum Gravity
Jibril Ben Achour, Marc Geiller, Karim Noui +1
We study the role of the Barbero-Immirzi parameter and the choice of connection in the construction of (a symmetry-reduced version of) loop quantum gravity. We start with the…
A Lorentz-Covariant Connection for Canonical Gravity
Marc Geiller, Marc Lachieze-Rey, Karim Noui +1
We construct a Lorentz-covariant connection in the context of first order canonical gravity with non-vanishing Barbero-Immirzi parameter. To do so, we start with the phase space fo…
The partial Bondi gauge: Gauge fixings and asymptotic charges
Marc Geiller, Céline Zwikel
In the companion paper [SciPost Phys. 13, 108 (2022), arXiv:2205.11401 [hep-th]] we have studied the solution space at null infinity for gravity in the partial Bondi gauge. This pa…
A new realization of quantum geometry
Benjamin Bahr, Bianca Dittrich, Marc Geiller
We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introduced flux formulation of loop quantum gravity. In this framew…
Corner symmetry and quantum geometry
Laurent Freidel, Marc Geiller, Wolfgang Wieland
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These char…
Hawking radiation by spherically-symmetric static black holes for all spins: I -- Teukolsky equations and potentials
Alexandre Arbey, Jérémy Auffinger, Marc Geiller +2
In the context of the dynamics and stability of black holes in modified theories of gravity, we derive the Teukolsky equations for massless fields of all spins in general spherical…
Extended actions, dynamics of edge modes, and entanglement entropy
Marc Geiller, Puttarak Jai-akson
In this work we propose a simple and systematic framework for including edge modes in gauge theories on manifolds with boundaries. We argue that this is necessary in order to achie…
Metric formulation of the simple theory of 3d massive gravity
Marc Geiller, Karim Noui
We have recently introduced a new and very simple action for three-dimensional massive gravity. This action is written in a first order formulation where the triad and the connecti…
Dynamical symmetries of homogeneous minisuperspace models
Marc Geiller, Etera R. Livine, Francesco Sartini
We investigate the phase space symmetries and conserved charges of homogeneous gravitational minisuperspaces. These (0+1)-dimensional reductions of general relativity are defined b…
Continuous formulation of the Loop Quantum Gravity phase space
Laurent Freidel, Marc Geiller, Jonathan Ziprick
In this paper, we study the discrete classical phase space of loop gravity, which is expressed in terms of the holonomy-flux variables, and show how it is related to the continuous…
Unimodular Loop Quantum Cosmology
Dah-Wei Chiou, Marc Geiller
Unimodular gravity is based on a modification of the usual Einstein-Hilbert action that allows one to recover general relativity with a dynamical cosmological constant. It also has…
Asymptotically-FLRW spacetimes
Andrea Campoleoni, Arnaud Delfante, Marc Geiller +1
We introduce three-dimensional asymptotically-FLRW spacetimes as a simplified setting in which to study asymptotic symmetries and radiation in cosmology. Their asymptotic symmetry…
Testing the imposition of the Spin Foam Simplicity Constraints
Marc Geiller, Karim Noui
We introduce a three-dimensional Plebanski action for the gauge group SO(4). In this model, the field satisfies quadratic simplicity constraints similar to that of the four-dim…