Searcharxiv⌕ Search

arXiv subjects

Marc Henneaux

Publications and source records attributed to Marc Henneaux.

At least 19 recordsLinked to original sources
arXiv2026

Logarithmic supertranslations as asymptotic symmetries of gravity at null infinity

Logarithmic supertranslations have been shown recently to be symmetries of the gravitational field at spatial infinity. We extend this work by proving explicitly that they are also symmetries at null infinity. We also show that the logarithmic supertranslation charges match at the ``corner" where spatial infinity and null infinity meet. This fully establishes that the asymptotic symmetry group of gravity in the asymptotically flat context contains the logarithmic supertranslations.

hep-th↗
arXiv2026

Carroll supergravities

The electric and magnetic carrollian limits of $N=1$ supergravity in $D=4$ spacetime dimensions are explicitly derived. The approach is general and applies also to extended supergravity models

hep-th↗
arXiv2026

Exact solution of two-dimensional Palatini Gauss-Bonnet theory on a strip

We analyze the two-dimensional Palatini Gauss-Bonnet theory on an infinite strip (product of a finite interval with the infinite line, corresponding to ``time"). The theory has only boundary degrees of freedom. Its phase space is the cotangent bundle to the group manifold of $SL(2,\mathbf{R})$, subject to a (first-class) constraint quadratic in the momenta. With the simplest choice of boundary Hamiltonian, namely $H = 0$, the theory is shown to describe geodesics on the group manifold of $SL(2,\mathbf{R})$, with a ``mass" determined by the Palatini Gauss-Bonnet coupling constant. Other choices of boundary Hamiltonians compatible with gauge invariance are also possible. The symmetry group contains (left and right) group translations on $SL(2,\mathbf{R})$. These are ``boundary symmetries" from the bulk point of view, one copy acting on one end of the interval, the other copy acting on the other end. Comments on the quantum theory are also given.

hep-th↗
arXiv2026

Palatini Gauss-Bonnet theory

We consider a class of models in even spacetime dimensions $2n$ which share many similarities with Chern-Simons theories in odd spacetime dimensions $2n+1$. The independent dynamical variables of these models are a $GL(2n)$-connection and a metric in internal space. The action is a polynomial of degree $n$ in the curvature of the connection, with indices saturated by means of the metric and the Levi-Civita tensor. We show that the theory has no local degree of freedom in $2$ spacetime dimensions ($n=1$), where it can be reformulated as a constrained $BF$ model, but that its dynamics is more intrincate in higher dimensions ($n>1$), where local degrees of freedom are present. We treat in detail the cases of $2$ and $4$ spacetime dimensions.}

hep-th↗
arXiv2025

BV-BRST Noether theorem

The BRST Noether theorem, or ``Noether's 1.5 theorem'', asserts the triviality of the BRST Noether current. We provide two proofs of this theorem that are both valid without restriction on the structure of the gauge theory, extending thereby previous proofs holding in the case of gauge theories for which the solution of the master equation is linear in the antifields. We also relate explicitly the BRST Noether current to the BRST master current appearing in the master equation.

hep-th↗
arXiv2025

Matching conditions at null infinity in the presence of logarithms: the role of advanced and retarded radiation

We provide a new perspective on the general matching conditions between the future of past null infinity and the past of future null infinity, emphasizing the impact of dominant logarithmic terms in the asymptotic expansion of the fields near null infinity. We explicitly consider the cases of a massless scalar field and of electromagnetism. Key in our derivation is the identification of the physical origin of these logarithms, which are associated with advanced and retarded radiation saturating the finite energy flux condition at null infinity (in a space of functions which is made precise). The matching conditions arise then from the requirement of Coulombic (i.e., $1/r$) behaviour at spatial infinity.

hep-th↗
arXiv2025

Wheeler-DeWitt equation and Bondi-Metzner-Sachs (BMS) symmetry

The Hamiltonian formulation of the BMS symmetry on spacelike hypersurfaces enables one to define its action on solutions of the Wheeler-DeWitt equation. Using the BRST reformulation of the theory, we provide operator expressions for the matrix elements of the BMS operators between Wheeler-DeWitt states. To that end, we construct the BRST-invariant extensions of the BMS generators, which form a BRST-extension of the BMS algebra.

hep-th↗
arXiv2025

Logarithmic angle-dependent gauge transformations at null infinity

Logarithmic angle-dependent gauge transformations are symmetries of electromagnetism that are canonically conjugate to the standard $\mathcal O(1)$ angle-dependent $u(1)$ transformations. They were exhibited a few years ago at spatial infinity. In this paper, we derive their explicit form at null infinity. We also derive the expression there of the associated "conserved" surface integrals. To that end, we provide a comprehensive analysis of the behaviour of the electromagnetic vector potential $A_μ$ in the vicinity of null infinity for generic initial conditions given on a Cauchy hypersurface. This behaviour is given by a polylogarithmic expansion involving both gauge-invariant logarithmic terms also present in the field strengths and gauge-variant logarithmic terms with physical content, which we identify. We show on which explicit terms, and how, do the logarithmic angle-dependent gauge transformations act. Other results of this paper are a derivation of the matching conditions for the Goldstone boson and for the conserved charges of the angle-dependent $u(1)$ asymptotic symmetries, as well as a clarification of a misconception concerning the non-existence of these angle-dependent $u(1)$ charges in the presence of logarithms at null infinity. We also briefly comment on higher spacetime dimensions.

hep-th↗
arXiv2024

Logarithmic matching between past infinity and future infinity: The massless scalar field

Matching conditions relating the fields at the future of past null infinity with the fields at the past of future null infinity play a central role in the analysis of asymptotic symmetries and conservation laws in asymptotically flat spacetimes. These matching conditions can be derived from initial data given on a Cauchy hypersurface by integrating forward and backward in time the field equations to leading order in an asymptotic expansion, all the way to future and past null infinities. The standard matching conditions considered in the literature are valid only in the case when the expansion near null infinity (which is generically polylogarithmic) has no dominant logarithmic term. This paper is the first in a series in which we derive the matching conditions for a massless scalar field with initial conditions leading to dominant logarithms at null infinity. We prove that these involve the opposite sign with respect to the usual matching conditions. We also analyse the matching of the angle-dependent conserved charges that follow from the asymptotic decay and Lorentz invariance. We show in particular that these are well defined and finite at null infinity even in the presence of leading logarithmic terms provided one uses the correct definitions. The free massless scalar field has the virtue of presenting the polylogarithmic features in a particularly clear setting that shows their inevitability, since there is no subtle gauge fixing issue or nonlinear intrincacies involved in the problem. We also consider the case of higher spacetime dimensions where fractional powers of $r$ (odd spacetime dimensions) or subdominant logarithmic terms (even spacetime dimensions) are present. Mixed matching conditions are then relevant. In subsequent papers, we will extend the analysis to the electromagnetic and the gravitational fields.

gr-qc↗
arXiv2024

Non-minimal couplings to $U(1)$-gauge fields and asymptotic symmetries

We analyse the asymptotic symmetries of electromagnetism non-minimally coupled to scalar fields, with non-minimal couplings of the Fermi type that occur in extended supergravity models. Our study is carried out at spatial infinity where minimal and non-minimal couplings exhibit very different asymptotic properties: while the former generically cannot be neglected at infinity, the latter can. Electromagnetic non-minimal couplings are in that respect similar to gravitational minimal couplings, which are also asymptotically subdominant. Because the non-minimally interacting model is asymptotic to the free one, its asymptotic symmetries are the same as the ones of the free theory, i.e., described by angle-dependent $u(1)$ gauge transformations. We also analyse the duality symmetry and show that it is broken to its compact subgroup by the asymptotic conditions. Finally, we consider logarithmic gauge transformations and use them to simplify the symmetry algebra.

hep-th↗
arXiv2024

Carroll swiftons

We construct Carroll-invariant theories with fields propagating outside the Carroll lightcone, i.e., at a speed strictly greater than zero (`Carroll swiftons'). We first consider models in flat Carroll spacetime in general dimensions, where we present scalar and vector Carroll swifton field theories. We then turn to the coupling to gravity and achieve in particular in two dimensions a Carroll invariant scalar swifton by coupling it suitably to Carroll dilaton gravity. Its backreaction on the geometry generates dynamical torsion.

hep-th↗
arXiv2024

Asymptotic symmetry algebra of Einstein gravity and Lorentz generators

The asymptotic symmetry algebra of four-dimensional Einstein gravity in the asymptotically flat context has been shown recently to be the direct sum of the Poincaré algebra and of an infinite-dimensional abelian algebra (with central charge) that includes the Bondi-Metzner-Sachs supertranslations. This result, obtained within the Hamiltonian formalism, yields a supertranslation invariant definition of the Lorentz generators (angular momentum and boosts). Definitions of Lorentz generators free from the ``supertranslation ambiguities'' have also been proposed recently at null infinity. We prove the equivalence of the two approaches for redefining the charges.

hep-th↗
arXiv2023

The BMS group in $D= 6$ spacetime dimensions

The asymptotic structure of gravity in $D=6$ spacetime dimensions is described at spatial infinity in the asymptotically flat context through Hamiltonian (ADM) methods. Special focus is given on the BMS supertranslation subgroup. It is known from previous studies that the BMS group contains more supertranslations as one goes from $D=4$ to $D=5$. Indeed, while the supertranslations are described by one single function of the angles in $D=4$, four such functions are neeeded in $D=5$. We consider the case $D=6$ with the aim of determining whether the number of supertranslations keeps increasing with the dimension or remains equal to the number found in $D=5$. We show that even though there is apparent room for more supertranslations, their number remains equal to the $D=5$ value (four): the potentially new supertranslations turn out to define proper gauge transformations corresponding to a redundancy in the description of the system. Critical in the analysis are the boundary conditions chosen to yield a well-defined canonical formalism. Given the computational (but not conceptual) complexity as one increases the dimension, we explicitly discuss the linearized theory and argue that asymptotically, this analysis provides the correct picture. We conclude by considering higher spacetime dimensions where we indicate that the number of physically relevant supertranslations remains equal to four independently of the dimension $\geq 5$.

hep-th↗
arXiv2023

Simplifying (super-)BMS algebras

We show that the non-linear BMS$_5$ symmetry algebra of asymptotically flat Einstein gravity in five dimensions, as well as the super-BMS$_4$ superalgebra of asymptotically flat supergravity, can be redefined so as to take a direct sum structure. In the new presentation of the (super-)algebra, angle-dependent translations and angle-dependent supersymmetry transformations commute with the (super-)Poincaré generators. We also explain in detail the structure and charge-integrability of asymptotic symmetries with symmetry parameters depending on the fields (through the charges themselves), a topic relevant for nonlinear asymptotic symmetry algebras.

hep-th↗
arXiv2023

A note on the asymptotic symmetries of electromagnetism

We extend the asymptotic symmetries of electromagnetism in order to consistently include angle-dependent $u(1)$ gauge transformations $ε$ that involve terms growing at spatial infinity linearly and logarithmically in $r$, $ε\sim a(θ, φ) r + b(θ, φ) \ln r + c(θ, φ)$. The charges of the logarithmic $u(1)$ transformations are found to be conjugate to those of the $\mathcal O(1)$ transformations (abelian algebra with invertible central term) while those of the $\mathcal O(r)$ transformations are conjugate to those of the subleading $\mathcal O(r^{-1})$ transformations. Because of this structure, one can decouple the angle-dependent $u(1)$ asymptotic symmetry from the Poincaré algebra, just as in the case of gravity: the generators of these internal transformations are Lorentz scalars in the redefined algebra. This implies in particular that one can give a definition of the angular momentum which is free from $u(1)$ gauge ambiguities. The change of generators that brings the asymptotic symmetry algebra to a direct sum form involves non linear redefinitions of the charges. Our analysis is Hamiltonian throughout and carried at spatial infinity.

hep-th↗
arXiv2022

Logarithmic supertranslations and supertranslation-invariant Lorentz charges

We extend the BMS(4) group by adding logarithmic supertranslations. This is done by relaxing the boundary conditions on the metric and its conjugate momentum at spatial infinity in order to allow logarithmic terms of carefully designed form in the asymptotic expansion, while still preserving finiteness of the action. Standard theorems of the Hamiltonian formalism are used to derive the (finite) generators of the logarithmic supertranslations. As the ordinary supertranslations, these depend on a function of the angles. Ordinary and logarithmic supertranslations are then shown to form an abelian subalgebra with non-vanishing central extension. Because of this central term, one can make nonlinear redefinitions of the generators of the algebra so that the pure supertranslations ($\ell >1$ in a spherical harmonic expansion) and the logarithmic supertranslations have vanishing brackets with all the Poincaré generators, and, in particular, transform in the trivial representation of the Lorentz group. The symmetry algebra is then the direct sum of the Poincaré algebra and the infinite-dimensional abelian algebra formed by the pure supertranslations and the logarithmic supertranslations (with central extension). The pure supertranslations are thus completely decoupled from the standard Poincaré algebra in the asymptotic symmetry algebra. This implies in particular that one can provide a definition of the angular momentum which is manifestly free from supertranslation ambiguities. An intermediate redefinition providing a partial decoupling of the pure and logarithmic supertranslations is also given.

hep-th↗