Marc Henneaux

Centro de Estudios Cientificos (CECs), Ciudad de Valdivía, Los Ríos, Chile

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Publications (231)886.05 Total impact

  • Source
    Marc Henneaux · Alfredo Perez · David Tempo · Ricardo Troncoso
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    ABSTRACT: We investigate the hypersymmetry bounds on the higher spin black hole parameters that follow from the asymptotic symmetry superalgebra in higher-spin anti-de Sitter gravity in three spacetime dimensions. We consider anti-de Sitter hypergravity for which the analysis is most transparent. This is a $osp(1\vert 4) \oplus osp(1\vert 4)$ Chern-Simons theory which contains, besides a spin-$2$ field, a spin-$4$ field and a spin-$5/2$ field. The asymptotic symmetry superalgebra is then the direct sum of two-copies of the hypersymmetric extension $W_{(2,\frac52,4)}$ of $W_{(2,4)}$, which contains fermionic generators of conformal weight $5/2$ and bosonic generators of conformal weight $4$ in addition to the Virasoro generators. Following standard methods, we derive bounds on the conserved charges from the anticommutator of the hypersymmetry generators. The hypersymmetry bounds are nonlinear and are saturated by the hypersymmetric black holes, which turn out to possess $1/4$-hypersymmetry and to be "extreme", where extremality can be defined in terms of the entropy: extreme black holes are those that fulfill the extremality bounds beyond which the entropy ceases to be a real function of the black hole parameters. We also extend the analysis to other $sp(4)$-solitonic solutions which are maximally (hyper)symmetric.
    Journal of High Energy Physics 06/2015; 2015(8). DOI:10.1007/JHEP08(2015)021 · 6.22 Impact Factor
  • Marc Henneaux · Axel Kleinschmidt · Victor Lekeu
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    ABSTRACT: We study the role of Chern--Simons couplings for the appearance of enhanced symmetries of Cremmer--Julia type in various theories. It is shown explicitly that for generic values of the Chern--Simons coupling there is only a parabolic Lie subgroup of symmetries after reduction to three space-time dimensions but that this parabolic Lie group gets enhanced to the full and larger Cremmer--Julia Lie group of hidden symmetries if the coupling takes a specific value. This is heralded by an enhanced isotropy group of the metric on the scalar manifold. Examples of this phenomenon are discussed as well as the relation to supersymmetry. Our results are also connected with rigidity theorems of Borel-like algebras.
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    Marc Henneaux · Victor Lekeu
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    ABSTRACT: We investigate the conjectured infinite-dimensional hidden symmetries of six-dimensional chiral supergravity coupled to two vector multiplets and two tensor multiplets, which is known to possess the $F_{4,4}$ symmetry upon dimensional reduction to three spacetime dimensions. Two things are done. (i) First, we analyze the geodesic equations on the coset space $F_{4,4}^{++}/K(F_{4,4}^{++})$ using the level decomposition associated with the subalgebra $\mathfrak{gl}(5)\oplus \mathfrak{sl}(2)$ of $F_{4,4}^{++}$ and show their equivalence with the bosonic equations of motion of six-dimensional chiral supergravity up to the level where the dual graviton appears. In particular, the self-duality condition on the chiral $2$-form is automatically implemented in the sense that no dual potential appears for that $2$-form, in contradistinction with what occurs for the non chiral $p$-forms. (ii) Second, we describe the $p$-form hierarchy of the model in terms of its $V$-duality Borcherds superalgebra, of which we compute the Cartan matrix.
    Journal of High Energy Physics 02/2015; 2015(3). DOI:10.1007/JHEP03(2015)056 · 6.22 Impact Factor
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    Andrea Campoleoni · Marc Henneaux
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    ABSTRACT: The asymptotic structure of three-dimensional higher-spin anti-de Sitter gravity is analyzed in the metric approach, in which the fields are described by completely symmetric tensors and the dynamics is determined by the standard Einstein-Fronsdal action improved by higher order terms that secure gauge invariance. Precise boundary conditions are given on the fields. The asymptotic symmetries are computed and shown to form a non-linear W-algebra, in complete agreement with what was found in the Chern-Simons formulation. The W-symmetry generators are two-dimensional traceless and divergenceless rank-s symmetric tensor densities of weight s (s = 2, 3, ...), while asymptotic symmetries emerge at infinity through the conformal Killing vector and conformal Killing tensor equations on the two-dimensional boundary, the solution space of which is infinite-dimensional. For definiteness, only the spin 3 and spin 4 cases are considered, but these illustrate the features of the general case: emergence of the W-extended conformal structure, importance of the improvement terms in the action that maintain gauge invariance, necessity of the higher spin gauge transformations of the metric, role of field redefinitions.
    Journal of High Energy Physics 12/2014; 1503:143. DOI:10.1007/JHEP03(2015)143 · 6.22 Impact Factor
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    ABSTRACT: Hypergravity is the theory in which the graviton, of spin-2, has a supersymmetric partner of spin-5/2. There are "no-go" theorems that prevent interactions in these higher spin theories. However, it appears that one can circumvent them by bringing in an infinite tower of higher spin fields. With this possibility in mind, we study herein the electric-magnetic duality invariance of hypergravity. The analysis is carried out in detail for the free theory of the spin-(2,5/2) multiplet, and it is indicated how it may be extended to the infinite tower of higher spins. Interactions are not considered. The procedure is the same that was employed recently for the spin-(3/2,2) multiplet of supergravity. One introduces new potentials ("prepotentials") by solving the constraints of the Hamiltonian formulation. In terms of the prepotentials, the action is written in a form in which its electric-magnetic duality invariance is manifest. The prepotential action is local, but the spacetime invariance is not manifest. Just as for the spin-2 and spin-(3/2,2) cases, the gauge symmetries of the prepotential action take a form similar to those of the free conformal theory of the same multiplet. The automatic emergence of gauge conformal invariance out of demand of manifest duality invariance, is yet another evidence of the subtle interplay between duality invariance and spacetime symmetry. We also compare and contrast the formulation with that of the analogous spin-(1,3/2) multiplet.
    Physical Review D 06/2014; 90(4). DOI:10.1103/PhysRevD.90.045029 · 4.86 Impact Factor
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    ABSTRACT: Three-dimensional spacetime with a negative cosmological constant has proven to be a remarkably fertile ground for the study of gravity and higher spin fields. The theory is topological and, since there are no propagating field degrees of freedom, the asymptotic symmetries become all the more crucial. For pure (2+1) gravity they consist of two copies of the Virasoro algebra. There exists a black hole which may be endowed with all the corresponding charges. The pure (2+1) gravity theory may be reformulated in terms of two Chern-Simons connections for sl(2,R). An immediate generalization containing gravity and a finite number of higher spin fields may be achieved by replacing sl(2,R) by sl(3,R) or, more generally, by sl(N,R). The asymptotic symmetries are then two copies of the so-called W_N algebra, which contains the Virasoro algebra as a subalgebra. The question then arises as to whether there exists a generalization of the standard pure gravity (2+1) black hole which would be endowed with all the W_N charges. The original pioneering proposal of a black hole along this line for N=3 turns out, as shown in this paper, to actually belong to the so called "diagonal embedding" of sl(2,R) in sl(3,R), and it is therefore endowed with charges of lower rather than higher spins. In contradistinction, we exhibit herein the most general black hole which belongs to the "principal embedding". It is endowed with higher spin charges, and possesses two copies of W_3 as its asymptotic symmetries. The most general diagonal embedding black hole is studied in detail as well, in a way in which its lower spin charges are clearly displayed. The extension to N>3 is also discussed. A general formula for the entropy of a generalized black hole is obtained in terms of the on-shell holonomies.
    Journal of High Energy Physics 04/2014; 2014(5). DOI:10.1007/JHEP05(2014)031 · 6.22 Impact Factor
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    Marc Henneaux · Gustavo Lucena Gomez · Rakibur Rahman
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    ABSTRACT: We investigate the cubic interactions of a massless higher-spin fermion with gravity in flat space and present covariant 2-s-s vertices, compatible with the gauge symmetries of the system, preserving parity. This explicit construction relies on the BRST deformation scheme that assumes locality and Poincare invariance. Consistent nontrivial cubic deformations exclude minimal gravitational coupling and may appear only with a number of derivatives constrained in a given range. Derived in an independent manner, our results do agree with those obtained from the light-cone formulation or inspired by string theory. We also show that none of the Abelian vertices deform the gauge transformations, while all the non-Abelian ones are obstructed in a local theory beyond the cubic order.
    Journal of High Energy Physics 10/2013; 2014(1). DOI:10.1007/JHEP01(2014)087 · 6.22 Impact Factor
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    Marc Henneaux · Alfredo Perez · David Tempo · Ricardo Troncoso
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    ABSTRACT: We indicate how to introduce chemical potentials for higher spin charges in higher spin anti-de Sitter gravity in a manner that manifestly preserves the original asymptotic W-symmetry. This is done by switching on a non-vanishing component of the connection along the temporal (thermal) circles. We first recall the procedure in the pure gravity case (no higher spin) where the only "chemical potentials" are the temperature and the chemical potential associated with the angular momentum. We then generalize to the higher spin case. We find that there is no tension with the W(N) or W(infinity) asymptotic algebra, which is obviously unchanged by the introduction of the chemical potentials. Our argument is non-perturbative.
    Journal of High Energy Physics 09/2013; 2013(12). DOI:10.1007/JHEP12(2013)048 · 6.22 Impact Factor
  • Physical Review D 09/2013; 88(6). DOI:10.1103/PhysRevD.88.069902 · 4.86 Impact Factor
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    Claudio Bunster · Marc Henneaux
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    ABSTRACT: Generalized gauge fields are tensor fields with mixed symmetries. For gravity and higher spins in dimensions greater than four, the fundamental field in the "magnetic representation" is a generalized gauge field. It is shown that the analog of a point source for a generalized gauge field is a special type of brane whose worldsheet has another brane interwoven into it: a current within a current. In the case of gravity in higher dimensions, this combined extended object is the generalization of a magnetic pole. The Dirac quantization condition for the "electric" and "magnetic" strengths holds.
    Physical Review D 08/2013; 88(8). DOI:10.1103/PhysRevD.88.085002 · 4.86 Impact Factor
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    Marc Henneaux · Rakibur Rahman
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    ABSTRACT: Interactions of gauge-invariant systems are severely constrained by several consistency requirements. One is the preservation of the number of gauge symmetries, another is causal propagation. For lower-spin fields, the emphasis is usually put on gauge invariance that happens to be very selective by itself. We demonstrate with an explicit example, however, that gauge invariance, albeit indispensable for constructing interactions, may not suffice as a consistency condition. The chosen example that exhibits this feature is the theory of a massless spin-3/2 field coupled to electromagnetism. We show that this system admits an electromagnetic background in which the spin-3/2 gauge field may move faster than light. Requiring causal propagation rules out otherwise allowed gauge-invariant couplings. This emphasizes the importance of causality analysis as an independent test for a system of interacting gauge fields. We comment on the implications of allowing new degrees of freedom and non-locality in a theory, on higher-derivative gravity and Vasiliev's higher-spin theories.
    Physical review D: Particles and fields 06/2013; 88(6). DOI:10.1103/PhysRevD.88.064013 · 4.86 Impact Factor
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    Claudio Bunster · Marc Henneaux · Sergio Hörtner
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    ABSTRACT: The linearized Einstein equations in D spacetime dimensions can be written as twisted self-duality equations expressing that the linearized curvature tensor of the graviton described by a rank-two symmetric tensor, is dual to the linearized curvature tensor of the "dual graviton" described by a tensor of (D-3,1) Young symmetry type. In the case of 4 dimensions, both the graviton and its dual are rank-two symmetric tensors (Young symmetry type (1,1)), while in the case of 11 space-time dimensions relevant to M-theory, the dual graviton is described by a tensor of (8,1) Young symmetry type. We provide in this paper an action principle that yields the twisted self-duality conditions as equations of motion, keeping the graviton and its dual on equal footing. In order to construct a local, quadratic, variational principle for the twisted linear self-duality equations, it is necessary to introduce two "prepotentials". These are also tensors of mixed Young symmetry types and are obtained by solving the Hamiltonian constraints of the Hamiltonian formulation either of the Pauli-Fierz action for the graviton or of the Curtright action for its dual, the resulting actions being identical. The prepotentials enjoy interesting gauge invariance symmetries, which are exhibited and generalize the gauge symmetries found in D=4. A variational principle where the basic variables are the original Pauli-Fierz field and its dual can also be given but contrary to the prepotential action, the corresponding action is non-local in space -- while remaining local in time. We also analyze in detail the Hamiltonian structure of the theory and show that the graviton and its dual are canonically conjugate in a sense made precise in the text.
    Physical review D: Particles and fields 06/2013; 88(6). DOI:10.1103/PhysRevD.88.064032 · 4.86 Impact Factor
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    Claudio Bunster · Marc Henneaux · Sergio Hörtner
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    ABSTRACT: A formulation of linearized gravity which is manifestly invariant under electric-magnetic duality rotations in the internal space of the metric and its dual, and which contains both metrics as basic variables (rather than the corresponding prepotentials), is derived. In this bimetric formulation, the variables have a more immediate geometrical significance, but the action is non-local in space, contrary to what occurs in the prepotential formulation. More specifically, one finds that: (i) the kinetic term is non-local in space (but local in time); (ii) the Hamiltonian is local in space and in time; (iii) the variables are subject to two Hamiltonian constraints, one for each metric.
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    Claudio Bunster · Marc Henneaux
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    ABSTRACT: We consider all possible dynamical theories which evolve two transverse vector fields out of a three-dimensional Euclidean hyperplane, subject to only two assumptions: (i) the evolution is local in space, and (ii) the theory is invariant under "duality rotations" of the vector fields into one another. The commutators of the Hamiltonian and momentum densities are shown to be necessarily those of the Poincare group or its zero signature contraction. Space-time structure thus emerges out of the principle of duality.
    Physical Review Letters 01/2013; 110(1):011603. DOI:10.1103/PhysRevLett.110.011603 · 7.51 Impact Factor
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    Claudio Bunster · Marc Henneaux · Sergio Hörtner
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    ABSTRACT: The concept of electric-magnetic duality can be extended to linearized gravity. It has indeed been established that in four dimensions, the Pauli-Fierz action (quadratic part of the Einstein-Hilbert action) can be cast in a form that is manifestly invariant under duality rotations in the internal 2-plane of the spacetime curvature and its dual. In order to achieve this manifestly duality-invariant form, it is necessary to introduce two "prepotentials", which form a duality multiplet. These prepotentials enjoy interesting gauge invariance symmetries, which are, for each, linearized diffeomorphisms and linearized Weyl rescalings. The purpose of this note is twofold: (i) To rewrite the manifestly-duality invariant action obtained in previous work in a way that makes its gauge invariances also manifest. (ii) To explicitly show that the equations of motion derived from that action can be interpreted as twisted self-duality conditions on the curvature tensors of the two metrics obtained from the two prepotentials.
    Journal of Physics A Mathematical and Theoretical 07/2012; 46(21). DOI:10.1088/1751-8113/46/21/214016 · 1.69 Impact Factor
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    Claudio Bunster · Marc Henneaux
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    ABSTRACT: For the free massless spin-one and spin-two field theories one may write the action in a form which is manifestly invariant under electric-magnetic duality. This is achieved by introducing new potentials through solving the constraints of the Hamiltonian formulation. The price for making electric-magnetic duality invariance manifest through this direct procedure is losing manifest Lorentz invariance. Both theories admit supersymmetric extensions, which make the bosonic fields and their corresponding fermionic partners to be parts of the same geometrical object, a supermultiplet. We present in this paper the supersymmetric extension of the manifestly electric-magnetic duality invariant actions for the photon and the photino; and for the graviton and the gravitino. In each case the spinor fields transform under electric-magnetic duality in a chiral manner. For the spin-tree-half field, which possesses a gauge invariance, it is necessary to bring in a spinor "prepotential". As in previous cases the introduction of additional potentials to solve the constraints increases the number of gauge invariances of the action, thus keeping the number of degrees of freedom unaltered. The similarity in the formulations for the photon-photino and graviton-gravitino systems is remarkable.
    Physical review D: Particles and fields 07/2012; 86(6). DOI:10.1103/PhysRevD.86.065018 · 4.86 Impact Factor
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    Marc Henneaux · Gustavo Lucena Gomez · Rakibur Rahman
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    ABSTRACT: We study the electromagnetic coupling of massless higher-spin fermions in flat space. Under the assumptions of locality and Poincare invariance, we employ the BRST-BV cohomological methods to construct consistent parity-preserving off-shell cubic 1-s-s vertices. Consistency and non-triviality of the deformations not only rule out minimal coupling, but also restrict the possible number of derivatives. Our findings are in complete agreement with, but derived in a manner independent from, the light-cone-formulation results of Metsaev and the string-theory-inspired results of Sagnotti-Taronna. We prove that any gauge-algebra-preserving vertex cannot deform the gauge transformations. We also show that in a local theory, without additional dynamical higher-spin gauge fields, the non-abelian vertices are eliminated by the lack of consistent second-order deformations.
    Journal of High Energy Physics 06/2012; 2012(8). DOI:10.1007/JHEP08(2012)093 · 6.22 Impact Factor
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    ABSTRACT: We consider (2 + 1)-dimensional (N, M)-extended higher-spin anti-de Sitter supergravity and study its asymptotic symmetries. The theory is described by the Chern-Simons action based on the real, infinite-dimensional higher-spin superalgebra $ {\text{sh}}{{\text{s}}^{\text{E}}}\left( {N|{2},\mathbb{R}} \right) \oplus \,{\text{sh}}{{\text{s}}^{\text{E}}}\left( {M|{2},\mathbb{R}} \right) $ . We specify consistent boundary conditions on the higher-spin super-gauge connection corresponding to asymptotically anti-de Sitter spacetimes. We then determine the residual gauge transformations that preserve these asymptotic conditions and compute their Poisson bracket algebra. We find that the asymptotic symmetry is enhanced from the higher- spin superalgebra to some (N, M)-extended super-W∞ nonlinear superalgebra. The latter has the same classical central charge as pure Einstein gravity. Special attention is paid to the (1,1) case. Truncation to the bosonic sector yields the previously found W∞ algebra, while truncation to the osp $ \left( {N|{2},\mathbb{R}} \right) $ sector reproduces the N -extended superconformal algebra (in its nonlinear version for N > 2). We discuss string theory realization of these higher-spin anti-de Sitter supergravity theories as well as relations to previous treatments of super-W∞ in the literature.
    Journal of High Energy Physics 06/2012; 2012(6). DOI:10.1007/JHEP06(2012)037 · 6.22 Impact Factor
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    ABSTRACT: We consider (2+1)-dimensional (N, M)-extended higher-spin anti-de Sitter supergravity and study its asymptotic symmetries. The theory is described by the Chern-Simons action based on a real, infinite-dimensional higher-spin superalgebra. We specify consistent boundary conditions on the higher-spin super-gauge connection corresponding to asymptotically anti-de Sitter spacetimes. We then determine the residual gauge transformations that preserve these asymptotic conditions and compute their Poisson bracket algebra. We find that the asymptotic symmetry is enhanced from the higher-spin superalgebra to some (N,M)-extended super-W(infinity) nonlinear superalgebra. The latter has the same classical central charge as pure Einstein gravity. Special attention is paid to the (1,1)-case. Truncation to the bosonic sector yields the previously found W(infinity) algebra, while truncation to the underlying finite-dimensional superalgebra reproduces the N-extended superconformal algebra (in its nonlinear version for N>2). We discuss string theory realization of these higher-spin anti-de Sitter supergravity theories as well as relations to previous treatments of super-W(infinity) in the literature.
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    Marc Henneaux · Axel Kleinschmidt · Hermann Nicolai
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    ABSTRACT: We consider the relation between higher spin gauge fields and real Kac-Moody Lie algebras. These algebras are obtained by double and triple extensions of real forms g_0 of the finite-dimensional simple algebras g arising in dimensional reductions of gravity and supergravity theories. Besides providing an exhaustive list of all such algebras, together with their associated involutions and restricted root diagrams, we are able to prove general properties of their spectrum of generators with respect to a decomposition of the triple extension of g_0 under its gravity subalgebra gl(D,R). These results are then combined with known consistent models of higher spin gauge theory to prove that all but finitely many generators correspond to non-propagating fields and there are no higher spin fields contained in the Kac-Moody algebra.
    General Relativity and Gravitation 10/2011; 44(7). DOI:10.1007/s10714-012-1369-9 · 1.73 Impact Factor

Publication Stats

13k Citations
886.05 Total Impact Points

Institutions

  • 1987–2015
    • Centro de Estudios Cientificos (CECs)
      Ciudad de Valdivía, Los Ríos, Chile
  • 2013
    • Max Planck Institute for Gravitational Physics (Albert-Einstein-Institute)
      Potsdam, Brandenburg, Germany
  • 1978–2013
    • Université Libre de Bruxelles
      • • Nuclear Physics and Mathematical Physics Unit
      • • Faculty of Sciences
      Bruxelles, Brussels Capital, Belgium
  • 2012
    • Universidad Andrés Bello
      CiudadSantiago, Santiago, Chile
  • 2010
    • Ecole Normale Supérieure de Paris
      • Laboratoire de Physique Théorique
      Lutetia Parisorum, Île-de-France, France
  • 1998
    • University of Barcelona
      • Departament d'Estructura i Constituents de la Matèria
      Barcelona, Catalonia, Spain
    • Queen Mary, University of London
      Londinium, England, United Kingdom
  • 1982–1998
    • University of Texas at Austin
      • Department of Physics
      Austin, Texas, United States
  • 1997
    • University of Santiago, Chile
      • Departamento de Física
      CiudadSantiago, Santiago, Chile
  • 1992
    • Pierre and Marie Curie University - Paris 6
      Lutetia Parisorum, Île-de-France, France