Papers by Nicolas Boulanger
Symmetry
Considering the Poincaré group ISO(d−1,1) in any dimension d>3, we characterise the coadjoint ... more Considering the Poincaré group ISO(d−1,1) in any dimension d>3, we characterise the coadjoint orbits that are associated with massive and massless particles of discrete spin. We also comment on how our analysis extends to the case of continuous spin.
Physics
Since the pioneering works of Newton (1643–1727), mechanics has been constantly reinventing itsel... more Since the pioneering works of Newton (1643–1727), mechanics has been constantly reinventing itself: reformulated in particular by Lagrange (1736–1813) then Hamilton (1805–1865), it now offers powerful conceptual and mathematical tools for the exploration of dynamical systems, essentially via the action-angle variables formulation and more generally through the theory of canonical transformations. We propose to the (graduate) reader an overview of these different formulations through the well-known example of Foucault’s pendulum, a device created by Foucault (1819–1868) and first installed in the Panthéon (Paris, France) in 1851 to display the Earth’s rotation. The apparent simplicity of Foucault’s pendulum is indeed an open door to the most contemporary ramifications of classical mechanics. We stress that adopting the formalism of action-angle variables is not necessary to understand the dynamics of Foucault’s pendulum. The latter is simply taken as well-known and simple dynamical s...
Physics of Particles and Nuclei Letters
We propose Chern-Simons models of fractional-spin fields interacting with ordinary tensorial high... more We propose Chern-Simons models of fractional-spin fields interacting with ordinary tensorial higher-spin fields and internal color gauge fields. For integer and half-integer values of the fractional spins, the model reduces to finite sets of fields modulo infinitedimensional ideals. We present the model on-shell using Fock-space representations of the underlying deformed-oscillator algebra.
Journal of High Energy Physics
Abelian vector fields non-minimally coupled to uncharged scalar fields arise in many contexts. We... more Abelian vector fields non-minimally coupled to uncharged scalar fields arise in many contexts. We investigate here through algebraic methods their consistent deformations ("gaugings"), i.e., the deformations that preserve the number (but not necessarily the form or the algebra) of the gauge symmetries. Infinitesimal consistent deformations are given by the BRST cohomology classes at ghost number zero. We parametrize explicitly these classes in terms of various types of global symmetries and corresponding Noether currents through the characteristic cohomology related to antifields and equations of motion. The analysis applies to all ghost numbers and not just ghost number zero. We also provide a systematic discussion of the linear and quadratic constraints on these parameters that follow from higher-order consistency. Our work is relevant to the gaugings of extended supergravities.
The European Physical Journal C
The status of classical stability in higher-derivative systems is still subject to discussions. I... more The status of classical stability in higher-derivative systems is still subject to discussions. In this note, we argue that, contrary to general belief, many higher-derivative systems are classically stable. The main tool to see this property are Nekhoroshev's estimates relying on the action-angle formulation of classical mechanics. The latter formulation can be reached provided the Hamiltonian is separable, which is the case for higher-derivative harmonic oscillators. The Pais-Uhlenbeck oscillators appear to be the only type of higher-derivative harmonic oscillator with stable classical dynamics. A wide class of interaction potentials can even be added that preserve classical stability. Adiabatic invariants are built in the case of a Pais-Uhlenbeck oscillator slowly changing in time; it is shown indeed that the dynamical stability is not jeopardised by the time-dependent perturbation.
Journal of High Energy Physics
After proving the impossibility of consistent non-minimal coupling of a real Rarita-Schwinger gau... more After proving the impossibility of consistent non-minimal coupling of a real Rarita-Schwinger gauge field to electromagnetism, we re-derive the necessity of introducing the graviton in order to couple a complex Rarita-Schwinger gauge field to electromagnetism, with or without a cosmological term, thereby obtaining N = 2 pure supergravity as the only possibility. These results are obtained with the BRST-BV deformation method around the flat and (A)dS backgrounds in 4 dimensions. The same method applied to n v vectors, N real spin-3/2 gauge fields and at most one real spinor field also requires gravity and yields N = 3 pure supergravity as well as N = 1 pure supergravity coupled to a vector supermultiplet, with or without cosmological terms. Independently of the matter content, we finally derive strong necessary quadratic constraints on the possible gaugings for an arbitrary number of spin-1 and spin-3/2 gauge fields, that are relevant for larger supergravities.
Journal of High Energy Physics
Cohomological techniques within the Batalin-Vilkovisky (BV) extension of the Becchi-Rouet-Stora-T... more Cohomological techniques within the Batalin-Vilkovisky (BV) extension of the Becchi-Rouet-Stora-Tyutin (BRST) formalism have proved invaluable for classifying consistent deformations of gauge theories. In this work we investigate the application of this idea to massive field theories in the Stueckelberg formulation. Starting with a collection of free massive vectors, we show that the cohomological method reproduces the cubic and quartic vertices of massive Yang-Mills theory. In the same way, taking a Fierz-Pauli graviton on a maximally symmetric space as the starting point, we are able to recover the consistent cubic vertices of nonlinear massive gravity. The formalism further sheds light on the characterization of Stueckelberg gauge theories, by demonstrating for instance that the gauge algebra of such models is necessarily Abelian and that they admit a Born-Infeld-like formulation in which the action is simply a combination of the gauge-invariant structures of the free theory.
Physics Letters B
We provide a unified treatment of electric-magnetic duality, at the action level and with manifes... more We provide a unified treatment of electric-magnetic duality, at the action level and with manifest Lorentz invariance, for massive, massless as well as partially-massless gravitons propagating in maximally symmetric spacetimes of any dimension n > 3. For massive and massless fields, we complete previous analyses that use parent-action techniques by giving dual descriptions that enable direct counting of physical degrees of freedom in the flat and massless limit. The same treatment is extended to the partiallymassless case, where the duality has been previously discussed in covariant form only at the level of the equations of motion. The nature of the dual graviton is therefore clarified for all values of the mass and of the cosmological constant.
Journal of Physics A: Mathematical and Theoretical
We first prove that, in Vasiliev's theory, the zero-form charges studied in 1103.2360 and 1208.38... more We first prove that, in Vasiliev's theory, the zero-form charges studied in 1103.2360 and 1208.3880 are twisted open Wilson lines in the noncommutative Z space. This is shown by mapping Vasiliev's higher-spin model on noncommutative Yang-Mills theory. We then prove that, prior to Bose-symmetrising, the cyclically-symmetric higherspin invariants given by the leading order of these n-point zero-form charges are equal to corresponding cyclically-invariant building blocks of n-point correlation functions of bilinear operators in free conformal field theories (CFT) in three dimensions. On the higher spin gravity side, our computation reproduces the results of 1210.7963 using an alternative method amenable to the computation of subleading corrections obtained by perturbation theory in normal order. On the free CFT side, our proof involves the explicit computation of the separate cyclic building blocks of the correlation functions of n conserved currents in arbitrary dimension d > 2 using polarization vectors, which is an original result. It is shown to agree, for d = 3 , with the results obtained in 1301.3123 in various dimensions and where polarization spinors were used.
New models of higher-spin gauge theories with dynamical 2-forms
Journal of High Energy Physics, 2014
We prove a generalized Flato-Fronsdal theorem for higher-order, scalar and spinor, singletons. In... more We prove a generalized Flato-Fronsdal theorem for higher-order, scalar and spinor, singletons. In the resulting infinite tower of bulk higher-spin fields, we point out the occurrence of partially-massless fields of all depths. This leads us to conjecture a holographic duality between a higher-spin gravity theory around AdS d+1 with the aforementioned spectrum of fields, and a free CF T d of fundamental (higher-order) scalar and spinor singletons. As a first check of this conjecture, we find that the total Casimir energy vanishes at one loop.
Journal of High Energy Physics
We derive the characters of all unitary irreducible representations of the (d+1)dimensional de Si... more We derive the characters of all unitary irreducible representations of the (d+1)dimensional de Sitter spacetime isometry algebra so(1, d + 1), and propose a dictionary between those representations and massive or (partially) massless fields on de Sitter spacetime. We propose a way of taking the flat limit of representations in (anti-) de Sitter spaces in terms of these characters, and conjecture the spectrum resulting from taking the flat limit of mixed-symmetry fields in de Sitter spacetime. We identify the equivalent of the scalar singleton for the de Sitter (dS) spacetime.
Journal of High Energy Physics, 2007
The general solutions of the Wess-Zumino consistency condition for the conformal (or Weyl, or tra... more The general solutions of the Wess-Zumino consistency condition for the conformal (or Weyl, or trace) anomalies are derived. The solutions are obtained, in arbitrary dimensions, by explicitly computing the cohomology of the corresponding Becchi-Rouet-Stora-Tyutin differential in the space of integrated local functions at ghost number unity. This provides a purely algebraic, regularizationindependent classification of the Weyl anomalies in arbitrary dimensions. The so-called type -A anomaly is shown to satisfy a non-trivial descent of equations, similarly to the non-Abelian chiral anomaly in Yang-Mills theory.
Physical Review Letters, 2007
Conformally invariant massless field systems involving only dimensionless parameters are known to... more Conformally invariant massless field systems involving only dimensionless parameters are known to describe particle physics at very high energy. In the presence of an external gravitational field, the conformal symmetry may generalize to Weyl invariance. However, the latter symmetry no longer survives after quantization: A Weyl anomaly appears. In this Letter, a purely algebraic understanding of the universal structure of the Weyl anomalies is presented. The results hold in arbitrary dimensions and independently of any regularization scheme.
Physical Review D, 2006
We show that Fronsdal's Lagrangian for a free massless spin-3 gauge field in Minkowski spacetime ... more We show that Fronsdal's Lagrangian for a free massless spin-3 gauge field in Minkowski spacetime is contained in a general Yang-Mills-like Lagrangian of metricaffine gravity (MAG), the gauge theory of the general affine group in the presence of a metric. Due to the geometric character of MAG, this can best be seen by using Vasiliev's frame formalism for higher-spin gauge fields in which the spin-3 frame is identified with the tracefree nonmetricity one-form associated with the shear gen- * peter.baekler@fh-duesseldorf.de † nicolas.boulanger@umh.ac.be ‡ hehl@thp.uni-koeln.de erators of GL(n, R). Furthermore, for specific gravitational gauge models in the framework of full nonlinear MAG, exact solutions are constructed, featuring propagating massless and massive spin-3 fields.
Journal of Mathematical Physics, 2005
On a (pseudo-) Riemannian manifold of dimension n 3, the space of tensors which transform covaria... more On a (pseudo-) Riemannian manifold of dimension n 3, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D, D] gives the conformally invariant Weyl tensor plus the Cotton tensor. So-called generalized connections and their transformation laws under diffeomorphisms and Weyl rescalings are also derived. These results are obtained by application of BRST techniques.
Fortschritte der Physik, 2002
We report yes-go and no-go results on consistent cross-couplings for a collection of gravitons. M... more We report yes-go and no-go results on consistent cross-couplings for a collection of gravitons. Motivated by the search of theories where multiplets of massless spin-two fields cross-interact, we look for all the consistent deformations of a positive sum of Pauli-Fierz actions. We also investigate the problem of deforming a (positive and negative) sum of linearized Weyl gravity actions and show explicitly that there exists multi-Weylgraviton theories. As the single-graviton Weyl theory, these theories do not have an energy bounded from below.
Classical and Quantum Gravity, 2015
We investigate the unfolded formulation of bosonic Lorentz tensor fields of arbitrary spin in AdS... more We investigate the unfolded formulation of bosonic Lorentz tensor fields of arbitrary spin in AdS 3 containing a parity breaking mass parameter. They include deformations of the linearisations of the Prokushkin-Vasiliev higher spin theory around its critical points. They also provide unfolded formulations of linearized topologically massive higher spin fields including their critical versions. The gauge invariant degrees of freedom are captured by infinite towers of zero forms. We also introduce two inequivalent sets of gauge potentials given by trace constrained Fronsdal fields and trace unconstrained metric-like fields.
Journal of High Energy Physics, 2015
We show that the particle states of Maxwell's theory, in D dimensions, can be represented in an i... more We show that the particle states of Maxwell's theory, in D dimensions, can be represented in an infinite number of ways by using different gauge fields. Using this result we formulate the dynamics in terms of an infinite set of duality relations which are first order in space-time derivatives. We derive a similar result for the three form in eleven dimensions where such a possibility was first observed in the context of E 11 . We also give an action formulation for some of the gauge fields. In this paper we give a pedagogical account of the Lorentz and gauge covariant formulation of the irreducible representations of the Poincaré group, used previously in higher spin theories, as this plays a key role in our constructions. It is clear that our results can be generalised to any particle.
We present a list of all inequivalent bosonic covariant free particle wave equations in a flat sp... more We present a list of all inequivalent bosonic covariant free particle wave equations in a flat spacetime of arbitrary dimension. The wave functions are assumed to have a finite number of components. We relate these wave equations to equivalent versions obtained following other approaches.
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Papers by Nicolas Boulanger