Publications (231)894.69 Total impact

Article: Higher Spin Conformal Geometry in Three Dimensions and Prepotentials for Higher Spin Gauge Fields
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ABSTRACT: We study systematically the conformal geometry of higher spin bosonic gauge fields in three spacetime dimensions. We recall the definition of the Cotton tensor for higher spins and establish a number of its properties that turn out to be key in solving in terms of prepotentials the constraint equations of the Hamiltonian (3 + 1) formulation of fourdimensional higher spin gauge fields. The prepotentials are shown to exhibit higher spin conformal symmetry. Just as for spins 1 and 2, they provide a remarkably simple, manifestly duality invariant formulation of the theory. While the higher spin conformal geometry is developed for arbitrary bosonic spin, we explicitly perform the Hamiltonian analysis and derive the solution of the constraints only in the illustrative case of spin 3. In a separate publication, the Hamiltonian analysis in terms of prepotentials is extended to all bosonic higher spins using the conformal tools of this paper, and the same emergence of higher spin conformal symmetry is confirmed.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the hypersymmetry bounds on the higher spin black hole parameters that follow from the asymptotic symmetry superalgebra in higherspin antide Sitter gravity in three spacetime dimensions. We consider antide Sitter hypergravity for which the analysis is most transparent. This is a $osp(1\vert 4) \oplus osp(1\vert 4)$ ChernSimons 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 twocopies 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 · 6.11 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the role of ChernSimons couplings for the appearance of enhanced symmetries of CremmerJulia type in various theories. It is shown explicitly that for generic values of the ChernSimons coupling there is only a parabolic Lie subgroup of symmetries after reduction to three spacetime dimensions but that this parabolic Lie group gets enhanced to the full and larger CremmerJulia 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 Borellike algebras.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the conjectured infinitedimensional hidden symmetries of sixdimensional 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 sixdimensional chiral supergravity up to the level where the dual graviton appears. In particular, the selfduality 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 · 6.11 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The asymptotic structure of threedimensional higherspin antide 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 EinsteinFronsdal 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 nonlinear Walgebra, in complete agreement with what was found in the ChernSimons formulation. The Wsymmetry generators are twodimensional traceless and divergenceless ranks 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 twodimensional boundary, the solution space of which is infinitedimensional. For definiteness, only the spin 3 and spin 4 cases are considered, but these illustrate the features of the general case: emergence of the Wextended 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 · 6.11 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Hypergravity is the theory in which the graviton, of spin2, has a supersymmetric partner of spin5/2. There are "nogo" 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 electricmagnetic 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 electricmagnetic duality invariance is manifest. The prepotential action is local, but the spacetime invariance is not manifest. Just as for the spin2 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 · 4.64 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Threedimensional 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 ChernSimons 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 socalled 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 onshell holonomies.Journal of High Energy Physics 04/2014; 2014(5). DOI:10.1007/JHEP05(2014)031 · 6.11 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the cubic interactions of a massless higherspin fermion with gravity in flat space and present covariant 2ss 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 lightcone formulation or inspired by string theory. We also show that none of the Abelian vertices deform the gauge transformations, while all the nonAbelian 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 · 6.11 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We indicate how to introduce chemical potentials for higher spin charges in higher spin antide Sitter gravity in a manner that manifestly preserves the original asymptotic Wsymmetry. This is done by switching on a nonvanishing 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 nonperturbative.Journal of High Energy Physics 09/2013; 2013(12). DOI:10.1007/JHEP12(2013)048 · 6.11 Impact Factor  Physical Review D 09/2013; 88(6). DOI:10.1103/PhysRevD.88.069902 · 4.64 Impact Factor

Article: Sources for Generalized Gauge Fields
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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 · 4.64 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Interactions of gaugeinvariant systems are severely constrained by several consistency requirements. One is the preservation of the number of gauge symmetries, another is causal propagation. For lowerspin 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 spin3/2 field coupled to electromagnetism. We show that this system admits an electromagnetic background in which the spin3/2 gauge field may move faster than light. Requiring causal propagation rules out otherwise allowed gaugeinvariant 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 nonlocality in a theory, on higherderivative gravity and Vasiliev's higherspin theories.Physical review D: Particles and fields 06/2013; 88(6). DOI:10.1103/PhysRevD.88.064013 · 4.86 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The linearized Einstein equations in D spacetime dimensions can be written as twisted selfduality equations expressing that the linearized curvature tensor of the graviton described by a ranktwo symmetric tensor, is dual to the linearized curvature tensor of the "dual graviton" described by a tensor of (D3,1) Young symmetry type. In the case of 4 dimensions, both the graviton and its dual are ranktwo symmetric tensors (Young symmetry type (1,1)), while in the case of 11 spacetime dimensions relevant to Mtheory, 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 selfduality 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 selfduality 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 PauliFierz 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 PauliFierz field and its dual can also be given but contrary to the prepotential action, the corresponding action is nonlocal 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  [Show abstract] [Hide abstract]
ABSTRACT: A formulation of linearized gravity which is manifestly invariant under electricmagnetic 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 nonlocal in space, contrary to what occurs in the prepotential formulation. More specifically, one finds that: (i) the kinetic term is nonlocal 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.  [Show abstract] [Hide abstract]
ABSTRACT: We consider all possible dynamical theories which evolve two transverse vector fields out of a threedimensional 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. Spacetime 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  [Show abstract] [Hide abstract]
ABSTRACT: The concept of electricmagnetic duality can be extended to linearized gravity. It has indeed been established that in four dimensions, the PauliFierz action (quadratic part of the EinsteinHilbert action) can be cast in a form that is manifestly invariant under duality rotations in the internal 2plane of the spacetime curvature and its dual. In order to achieve this manifestly dualityinvariant 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 manifestlyduality 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 selfduality 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:10.1088/17518113/46/21/214016 · 1.58 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: For the free massless spinone and spintwo field theories one may write the action in a form which is manifestly invariant under electricmagnetic duality. This is achieved by introducing new potentials through solving the constraints of the Hamiltonian formulation. The price for making electricmagnetic 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 electricmagnetic duality invariant actions for the photon and the photino; and for the graviton and the gravitino. In each case the spinor fields transform under electricmagnetic duality in a chiral manner. For the spintreehalf 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 photonphotino and gravitongravitino systems is remarkable.Physical review D: Particles and fields 07/2012; 86(6). DOI:10.1103/PhysRevD.86.065018 · 4.86 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the electromagnetic coupling of massless higherspin fermions in flat space. Under the assumptions of locality and Poincare invariance, we employ the BRSTBV cohomological methods to construct consistent paritypreserving offshell cubic 1ss vertices. Consistency and nontriviality 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 lightconeformulation results of Metsaev and the stringtheoryinspired results of SagnottiTaronna. We prove that any gaugealgebrapreserving vertex cannot deform the gauge transformations. We also show that in a local theory, without additional dynamical higherspin gauge fields, the nonabelian vertices are eliminated by the lack of consistent secondorder deformations.Journal of High Energy Physics 06/2012; 2012(8). DOI:10.1007/JHEP08(2012)093 · 6.11 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider (2 + 1)dimensional (N, M)extended higherspin antide Sitter supergravity and study its asymptotic symmetries. The theory is described by the ChernSimons action based on the real, infinitedimensional higherspin 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 higherspin supergauge connection corresponding to asymptotically antide 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 superW∞ 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 higherspin antide Sitter supergravity theories as well as relations to previous treatments of superW∞ in the literature.Journal of High Energy Physics 06/2012; 2012(6). DOI:10.1007/JHEP06(2012)037 · 6.11 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider (2+1)dimensional (N, M)extended higherspin antide Sitter supergravity and study its asymptotic symmetries. The theory is described by the ChernSimons action based on a real, infinitedimensional higherspin superalgebra. We specify consistent boundary conditions on the higherspin supergauge connection corresponding to asymptotically antide 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 higherspin superalgebra to some (N,M)extended superW(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 finitedimensional superalgebra reproduces the Nextended superconformal algebra (in its nonlinear version for N>2). We discuss string theory realization of these higherspin antide Sitter supergravity theories as well as relations to previous treatments of superW(infinity) in the literature.
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Institutions

19862015

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


19782015

Université Libre de Bruxelles
 • Nuclear Physics and Mathematical Physics Unit
 • Faculty of Sciences
Bruxelles, Brussels Capital, Belgium


2012

Universidad Andrés Bello
CiudadSantiago, Santiago, Chile


1998

University of Barcelona
 Departament d'Estructura i Constituents de la Matèria
Barcelona, Catalonia, Spain 
Queen Mary, University of London
Londinium, England, United Kingdom


19821998

University of Texas at Austin
 Department of Physics
Austin, Texas, United States


1992

Pierre and Marie Curie University  Paris 6
Lutetia Parisorum, ÎledeFrance, France
