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Nicolas Boulanger

Publications and source records attributed to Nicolas Boulanger.

90 records · Page 5Linked to original sources
arXiv2006

On Killing tensors and cubic vertices in higher-spin gauge theories

The problem of determining all consistent non-Abelian local interactions is reviewed in flat space-time. The antifield-BRST formulation of the free theory is an efficient tool to address this problem. Firstly, it allows to compute all on-shell local Killing tensor fields, which are important because of their deep relationship with higher-spin algebras. Secondly, under the sole assumptions of locality and Poincare invariance, all non-trivial consistent deformations of a sum of spin-three quadratic actions deforming the Abelian gauge algebra were determined. They are compared with lower-spin cases.

hep-th↗
arXiv2005

A Weyl-covariant tensor calculus

On a (pseudo-) Riemannian manifold of dimension n > 2, 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.

hep-th↗
arXiv2004

No Self-Interaction for Two-Column Massless Fields

We investigate the problem of introducing consistent self-couplings in free theories for mixed tensor gauge fields whose symmetry properties are characterized by Young diagrams made of two columns of arbitrary (but different) lengths. We prove that, in flat space, these theories admit no local, Poincaré-invariant, smooth, self-interacting deformation with at most two derivatives in the Lagrangian. Relaxing the derivative and Lorentz-invariance assumptions, there still is no deformation that modifies the gauge algebra, and in most cases no deformation that alters the gauge transformations.Our approach is based on a BRST-cohomology deformation procedure.

hep-th↗
arXiv2004

Consistent deformations of [p,p]-type gauge field theories

Using BRST-cohomological techniques, we analyze the consistent deformations of theories describing free tensor gauge fields whose symmetries are represented by Young tableaux made of two columns of equal length p, p>1. Under the assumptions of locality and Poincare invariance, we find that there is no consistent deformation of these theories that non-trivially modifies the gauge algebra and/or the gauge transformations. Adding the requirement that the deformation contains no more than two derivatives, the only possible deformation is a cosmological-constant-like term.

hep-th↗
arXiv2003

Mixed symmetry gauge fields in a flat background

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.

hep-th↗
arXiv2003

Tensor gauge fields in arbitrary representations of GL(D,R) : duality & Poincare lemma

Using a mathematical framework which provides a generalization of the de Rham complex (well-designed for p-form gauge fields), we study the gauge structure and duality properties of theories for free gauge fields transforming in arbitrary irreducible representations of GL(D,R). We prove a generalization of the Poincare lemma which enables us to solve the above-mentioned problems in a systematic and unified way.

hep-th↗
arXiv2003

A note on spin-s duality

Duality is investigated for higher spin ($s \geq 2$), free, massless, bosonic gauge fields. We show how the dual formulations can be derived from a common "parent", first-order action. This goes beyond most of the previous treatments where higher-spin duality was investigated at the level of the equations of motion only. In D=4 spacetime dimensions, the dual theories turn out to be described by the same Pauli-Fierz (s=2) or Fronsdal ($s \geq 3$) action (as it is the case for spin 1). In the particular s=2 D=5 case, the Pauli-Fierz action and the Curtright action are shown to be related through duality. A crucial ingredient of the analysis is given by the first-order, gauge-like, reformulation of higher spin theories due to Vasiliev.

hep-th↗
arXiv2003

Consistent deformations of dual formulations of linearized gravity: A no-go result

The consistent, local, smooth deformations of the dual formulation of linearized gravity involving a tensor field in the exotic representation of the Lorentz group with Young symmetry type (D-3,1) (one column of length D-3 and one column of length 1) are systematically investigated. The rigidity of the Abelian gauge algebra is first established. We next prove a no-go theorem for interactions involving at most two derivatives of the fields.

hep-th↗
arXiv2003

Massless spin-two field S-duality

We present a review of the homological algebra tools involved in the standard de Rham theory and their subsequent generalizations relevant for the understanding of free massless higher spin gauge structure. M-theory arguments suggest the existence of an extension of (Abelian) S-duality symmetry for non-Abelian gauge theories, like the four dimensional Yang-Mills or Einstein theories. Some no-go theorems prove that this extension, if it exists, should fall outside the scope of local perturbative field theory.

hep-th↗
arXiv2003

On geometric equations and duality for free higher spins

We provide a general scheme for dualizing higher-spin gauge fields in arbitrary irreducible representations of GL(D,R). We also give a recipe for constructing Fronsdal-like field equations and Lagrangians for such exotic fields.

hep-th↗
arXiv2002

A note on the uniqueness of D=4 N=1 Supergravity

We investigate in 4 spacetime dimensions, all the consistent deformations of the lagrangian ${\cal L}_2+{\cal L}_{3/2}$, which is the sum of the Pauli-Fierz lagrangian ${\cal L}_2$ for a free massless spin 2 field and the Rarita-Schwinger lagrangian ${\cal L}_{3/2}$ for a free massless spin 3/2 field. Using BRST cohomogical techniques, we show, under the assumptions of locality, Poincaré invariance, conservation of the number of gauge symmetries and the number of derivatives on each fields, that N=1 D=4 supergravity is the only consistent interaction between a massless spin 2 and a massless spin 3/2 field. We do not assume general covariance. This follows automatically, as does supersymmetry invariance. Various cohomologies related to conservations laws are also given.

gr-qc↗
arXiv2002

Conformal (super)gravities with several gravitons

We construct consistent interacting gauge theories for M conformal massless spin-2 fields ("Weyl gravitons") with the following properties: (i) in the free limit, each field fulfills the equation ${\cal B}^{μν} = 0$, where ${\cal B}^{μν}$ is the linearized Bach tensor, (ii) the interactions contain no more than four derivatives, just as the free action and (iii) the internal metric for the Weyl gravitons is not positive definite. The interacting theories are obtained by gauging appropriate non-semi-simple extensions of the conformal algebra $so(4,2)$ with commutative, associative algebras of dimension M. By writing the action in terms of squares of supercurvatures, supersymmetrization is immediate and leads to consistent conformal supergravities with M interacting gravitons.

hep-th↗
arXiv2001

Multi-graviton theories : yes-go and no-go results

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-Weyl-graviton theories. As the single-graviton Weyl theory, these theories do not have an energy bounded from below.

hep-th↗
arXiv2001

An Exotic Theory of Massless Spin-Two Fields in Three Dimensions

It is a general belief that the only possible way to consistently deform the Pauli-Fierz action, changing also the gauge algebra, is general relativity. Here we show that a different type of deformation exists in three dimensions if one allows for PT non-invariant terms. The new gauge algebra is different from that of diffeomorphisms. Furthermore, this deformation can be generalized to the case of a collection of massless spin-two fields. In this case it describes a consistent interaction among them.

hep-th↗
arXiv2000

Inconsistency of interacting, multi-graviton theories

We investigate, in any spacetime dimension >=3, the problem of consistent couplings for a finite collection of massless, spin-2 fields described, in the free limit, by a sum of Pauli-Fierz actions. We show that there is no consistent (ghost-free) coupling, with at most two derivatives of the fields, that can mix the various "gravitons". In other words, there are no Yang-Mills-like spin-2 theories. The only possible deformations are given by a sum of individual Einstein-Hilbert actions. The impossibility of cross-couplings subsists in the presence of scalar matter. Our approach is based on the BRST-based deformation point of view and uses results on the so-called "characteristic cohomology" for massless spin-2 fields which are explained in detail.

hep-th↗
arXiv2000

No consistent cross-interactions for a collection of massless spin-2 fields

We report a no-go theorem excluding consistent cross-couplings for a collection of massless, spin-2 fields described, in the free limit, by the sum of Pauli-Fierz actions (one for each field). We show that, in spacetime dimensions >2, there is no consistent coupling, with at most two derivatives of the fields, that can mix the various "gravitons". The only possible deformations are given by the sum of individual Einstein-Hilbert actions (one for each field) with cosmological terms. Our approach is based on the BRST-based deformation point of view.

hep-th↗