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55

Sep 22, 2013
09/13

by
Nicolas Boulanger

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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...

Source: http://arxiv.org/abs/hep-th/0111216v1

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61

Sep 21, 2013
09/13

by
Nicolas Boulanger

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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...

Source: http://arxiv.org/abs/0706.0340v1

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58

Sep 18, 2013
09/13

by
Nicolas Boulanger

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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, regularization-independent classification of the Weyl anomalies in arbitrary dimensions. The so-called type-A anomaly is...

Source: http://arxiv.org/abs/0704.2472v1

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134

Sep 24, 2013
09/13

by
Nicolas Boulanger

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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.

Source: http://arxiv.org/abs/hep-th/0412314v2

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5.0

Jun 22, 2021
06/21

by
nicolas BOULANGER (nicolas258pro)

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Designed up this dealer button to use in home games or have just as something laying around for any poker fan. It was inspired by a dealer button in Pokerstars VR. Printing: Ring - Infil to add weight, supports needed for spade inset. Letter embossing doesn't need it. Spade - Infil to add weight, no supports Letters - Print flat, already scaled to fit nicely in the embossing Star - Infil to add weight. Full print with 4x4x4 walls/top/bottom and 38% infil came to about 48g in weight. Glue in...

Topics: stl, thingiverse, Automotive

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6.0

Jan 3, 2021
01/21

by
nicolas BOULANGER (nicolas258pro)

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pour remplacer les support de plateau de rummikub lorsqu'ils sont cassés. impression en PLA - 30% de remplissage . j'ai joint le fichier source si vous voulez le modifier avec freecad 0.19

Topics: stl, support, Games, plateau, thingiverse, Rummikub, PIED

1
1.0

Sep 4, 2022
09/22

by
Nicolas Boulanger (nicobelgium)

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Customized version of https://www.thingiverse.com/thing:5458888 Created with Customizer! https://www.thingiverse.com/apps/customizer/run?thing_id=5458888

Topics: Electronics, customized, thingiverse, stl

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49

Sep 18, 2013
09/13

by
Xavier Bekaert; Nicolas Boulanger

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Quadratic, second-order, non-local actions for tensor gauge fields transforming in arbitrary irreducible representations of the general linear group in D-dimensional Minkowski space are explicitly written in a compact form by making use of Levi-Civita tensors. The field equations derived from these actions ensure the propagation of the correct massless physical degrees of freedom and are shown to be equivalent to non-Lagrangian local field equations proposed previously. Moreover, these actions...

Source: http://arxiv.org/abs/hep-th/0606198v2

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293

Sep 18, 2013
09/13

by
Xavier Bekaert; Nicolas Boulanger

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An extensive group-theoretical treatment of linear relativistic wave equations on Minkowski spacetime of arbitrary dimension D>2 is presented in these lecture notes. To start with, the one-to-one correspondence between linear relativistic wave equations and unitary representations of the isometry group is reviewed. In turn, the method of induced representations reduces the problem of classifying the representations of the Poincare group ISO(D-1,1) to the classication of the representations...

Source: http://arxiv.org/abs/hep-th/0611263v1

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54

Sep 19, 2013
09/13

by
Xavier Bekaert; Nicolas Boulanger

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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.

Source: http://arxiv.org/abs/hep-th/0208058v2

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54

Sep 20, 2013
09/13

by
Nicolas Boulanger; Johanna Erdmenger

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Following a purely algebraic procedure, we provide an exhaustive classification of local Weyl-invariant scalar densities in dimension D=8.

Source: http://arxiv.org/abs/hep-th/0405228v2

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44

Sep 18, 2013
09/13

by
Xavier Bekaert; Nicolas Boulanger

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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...

Source: http://arxiv.org/abs/hep-th/0212131v2

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48

Sep 20, 2013
09/13

by
Xavier Bekaert; Nicolas Boulanger

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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.

Source: http://arxiv.org/abs/hep-th/0301243v1

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Sep 21, 2013
09/13

by
Nicolas Boulanger; Ingo Kirsch

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We continue the work of hep-th/0503024 in which gravity is considered as the Goldstone realization of a spontaneously broken diffeomorphism group. We complete the discussion of the coset space Diff(d,R)/SO(1,d-1) formed by the d-dimensional group of analytic diffeomorphisms and the Lorentz group. We find that this coset space is parameterized by coordinates, a metric and an infinite tower of higher-spin-like or generalized connections. We then study effective actions for the corresponding...

Source: http://arxiv.org/abs/hep-th/0602225v2

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5.0

Jun 28, 2018
06/18

by
Fabien Buisseret; Nicolas Boulanger

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Relying on an effective-string approach in which glueballs --- bound states of pure Yang-Mills theory --- are modelled by closed strings, we give arguments suggesting that anyonic glueballs, \textit{i.e.} glueballs with arbitrary spin, may exist in $(2+1)$-$\,$dimensional Yang-Mills theory. We then focus on the large$\,$-$N_c$ limit of $SU$($N_c$) Yang-Mills theory and show that our model leads to a mass spectrum in good agreement with lattice data in the scalar sector, while it predicts the...

Topics: High Energy Physics - Lattice, High Energy Physics - Theory

Source: http://arxiv.org/abs/1509.09312

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49

Sep 18, 2013
09/13

by
Nicolas Boulanger; Per Sundell

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We provide Vasiliev's fully nonlinear equations of motion for bosonic gauge fields in four spacetime dimensions with an action principle. We first extend Vasiliev's original system with differential forms in degrees higher than one. We then derive the resulting duality-extended equations of motion from a variational principle based on a generalized Hamiltonian sigma-model action. The generalized Hamiltonian contains two types of interaction freedoms: One set of functions that appears in the...

Source: http://arxiv.org/abs/1102.2219v2

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4.0

Jan 4, 2021
01/21

by
Nicolas Boulanger (Will_Maykit)

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Hi, this piece is used in a chest to a Peugeot 106, is it for replace broken pieces of the quarter-deck. (you need to mirror to get the second symmetric piece) . . Bonjour, ces pièces sont les axes de la plage arrière d'une Peugeot 106.

Topics: coffre, stl, plage, chest, Vehicles, auto, thingiverse, quarter-deck

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49

Jul 20, 2013
07/13

by
Nicolas Boulanger; Serge Leclercq

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We solve the problem of constructing consistent first-order cross-interactions between spin-2 and spin-3 massless fields in flat spacetime of arbitrary dimension n > 3 and in such a way that the deformed gauge algebra is non-Abelian. No assumptions are made on the number of derivatives involved in the Lagrangian, except that it should be finite. Together with locality, we also impose manifest Poincare invariance, parity invariance and analyticity of the deformations in the coupling constants.

Source: http://arxiv.org/abs/hep-th/0609221v3

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58

Sep 22, 2013
09/13

by
Xavier Bekaert; Nicolas Boulanger

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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.

Source: http://arxiv.org/abs/hep-th/0310209v2

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116

Sep 18, 2013
09/13

by
Nicolas Boulanger; Olaf Hohm

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We give a reformulation of non-linear Einstein gravity, which contains the dual graviton together with the ordinary metric and a shift gauge field. The metric does not enter through a `kinetic' Einstein-Hilbert term, but via topological couplings, and so the theory does not lead to a doubling of degrees of freedom. The field equations take the form of first-order duality relations. We analyze the gauge symmetries and comment on their meaning with regard to the E11 proposal.

Source: http://arxiv.org/abs/0806.2775v4

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64

Sep 18, 2013
09/13

by
Nicolas Boulanger; Mboyo Esole

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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, Poincar\'e invariance, conservation of the number of gauge symmetries and the number of derivatives on each...

Source: http://arxiv.org/abs/gr-qc/0110072v2

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5.0

Mar 31, 2021
03/21

by
Nicolas Boulanger (Will_Maykit)

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Thx 4frica :) I'm used this art to complete my water bottle design, diameter inside is 28.8mm on 11mm height (it's a classic plastic cap wine bottle I've used) STL and GCODE inside enjoy.

Topics: Bottle_cap, thingiverse, rose, winebottle, Kitchen & Dining, stl, bottle

4
4.0

Mar 10, 2021
03/21

by
Nicolas Boulanger (Will_Maykit)

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hello, my dad claim to me this piece, because it seems to break easily by mistake... --------- bonjour, mon père m'a réclamé cette pièce qui casse facilement a priori...

Topics: table_saw, stl, thingiverse, Machine Tools

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69

Sep 18, 2013
09/13

by
Xavier Bekaert; Nicolas Boulanger

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In free completely symmetric tensor gauge field theories on Minkowski space-time, all gauge invariant functions and Killing tensor fields are computed, both on-shell and off-shell. These problems are addressed in the metric-like formalisms.

Source: http://arxiv.org/abs/hep-th/0505068v3

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74

Sep 21, 2013
09/13

by
Nicolas Boulanger; Sandrine Cnockaert

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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...

Source: http://arxiv.org/abs/hep-th/0402180v2

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6.0

Jun 29, 2018
06/18

by
Thomas Basile; Nicolas Boulanger

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We derive and spell out the structure constants of the $\mathbb{Z}_2$-graded algebra $\mathfrak{shs}[\lambda]\,$ by using deformed-oscillators techniques in $Aq(2;\nu)\,$, the universal enveloping algebra of the Wigner-deformed Heisenberg algebra in 2 dimensions. The use of Weyl ordering of the deformed oscillators is made throughout the paper, via the symbols of the operators and the corresponding associative, non-commutative star product. The deformed oscillator construction was used by...

Topics: High Energy Physics - Theory, Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1604.04510

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4.0

Mar 19, 2021
03/21

by
Nicolas Boulanger (Will_Maykit)

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hello, voici une copie plus longue des rails droits fournis dans la boite du petit train de chez Gifi. (longueur 217mm environ) ***** hey, this is a copy but more longer of a rail train in a box bought in a Gifi store (france).

Topics: extention, thingiverse, train, toy, Toy & Game Accessories, stl

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5.0

Apr 1, 2021
04/21

by
Nicolas Boulanger (Will_Maykit)

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Hey, I was very frustrated to not have an elegant holder to get my taps on hand, so I made this, and now my coworkers are jealous ;) I put STL, F3D, screens, full package. You can easily edit what you want (by the way sorry for the fusion's timeline I'm very newbie) ------------------ Salut, petit support de tarauds qui va de M2 à M16, tous les fichiers sont dispo, vous pourrez modifier comme bon vous semble. °°° free to kiff.

Topics: CNC_Machine, Toolbox, tool_holder, taps, thingiverse, Tool Holders & Boxes, support, holder,...

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50

Sep 18, 2013
09/13

by
Nicolas Boulanger; Leonardo Gualtieri

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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...

Source: http://arxiv.org/abs/hep-th/0012003v3

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105

Jul 20, 2013
07/13

by
Nicolas Boulanger; E. D. Skvortsov

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Nonabelian Fradkin-Vasiliev cubic interactions for dual-graviton-like gauge fields with gravity and themselves are constructed in anti-de Sitter spacetime. The Young diagrams of gauge potentials have shapes of 'tall-hooks', i.e. two columns the second of height one. The underlying nonabelian algebra is a Clifford algebra with the anti-de Sitter signature. We also discuss the universal enveloping realization of higher-spin algebras, showing that there is a one-parameter family of algebras...

Source: http://arxiv.org/abs/1107.5028v3

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54

Sep 21, 2013
09/13

by
Xavier Bekaert; Nicolas Boulanger; Sandrine Cnockaert

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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, Poincar\'e-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...

Source: http://arxiv.org/abs/hep-th/0407102v1

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21

Jun 26, 2018
06/18

by
Nicolas Boulanger; Per Sundell; Peter West

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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 E11. We also give an action formulation for some of the gauge fields. In...

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1502.07909

54
54

Sep 18, 2013
09/13

by
Xavier Bekaert; Nicolas Boulanger; Marc Henneaux

texts

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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.

Source: http://arxiv.org/abs/hep-th/0210278v2

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56

Sep 22, 2013
09/13

by
Nicolas Boulanger; Carlo Iazeolla; Per Sundell

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We present some generalities of unfolded on-shell dynamics that are useful in analysing the BMV conjecture for mixed-symmetry fields in constantly curved backgrounds. In particular we classify the Lorentz-covariant Harish-Chandra modules generated from primary Weyl tensors of arbitrary mass and shape, and in backgrounds with general values of the cosmological constant. We also discuss the unfolded notion of local degrees of freedom in theories with and without gravity and with and without...

Source: http://arxiv.org/abs/0812.3615v2

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12

Jun 27, 2018
06/18

by
Nicolas Boulanger; Per Sundell; Mauricio Valenzuela

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We provide a necessary and sufficient condition for the consistency of the supertrace, through the existence of a certain ground state projector. We build this projector and check its properties to the first two orders in the number operator and to all orders in the deformation parameter. We then find the relation between the gravitational and internal gauge couplings in the resulting unified three-dimensional Chern--Simons theory for Blencowe--Vasiliev higher spin gravity coupled to fractional...

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1504.04286

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18

Jun 27, 2018
06/18

by
Nicolas Boulanger; Ergin Sezgin; Per Sundell

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We provide an off-shell formulation of four-dimensional higher spin gravity based on a covariant Hamiltonian action on an open nine-dimensional Poisson manifold whose boundary consists of the direct product of spacetime and a noncommutative twistor space of S^2 x S^2 topology. The fundamental field is a superconnection consisting of even and odd differential forms valued in the odd and even sectors of a 3-graded associative algebra given by the direct product of an eight-dimensional Frobenius...

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1505.04957

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67

Sep 18, 2013
09/13

by
Nicolas Boulanger; Sandrine Cnockaert; Marc Henneaux

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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)....

Source: http://arxiv.org/abs/hep-th/0306023v3

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6.0

Jun 28, 2018
06/18

by
Thomas Basile; Xavier Bekaert; Nicolas Boulanger

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We investigate the problem of finding a pure spin-connection formulation of General Relativity with non-vanishing cosmological constant. We first revisit the problem at the linearised level and find that the pure spin-connection, quadratic Lagrangian, takes a form reminiscent to Weyl gravity, given by the square of a Weyl-like tensor. Upon Hodge dualisation, we show that the dual gauge field in (A)dS$_D$ transforms under $GL(D)$ in the same representation as a massive graviton in the flat...

Topics: General Relativity and Quantum Cosmology, High Energy Physics - Theory

Source: http://arxiv.org/abs/1512.09060

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46

Sep 19, 2013
09/13

by
Nicolas Boulanger; Fabien Buisseret; Philippe Spindel

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We investigate the quantum motion of a neutral Dirac particle bouncing on a mirror in curved spacetime. We consider different geometries: Rindler, Kasner-Taub and Schwarzschild, and show how to solve the Dirac equation by using geometrical methods. We discuss, in a first-quantized framework, the implementation of appropriate boundary conditions. This leads us to consider a Robin boundary condition that gives the quantization of the energy, the existence of bound states and of critical heights...

Source: http://arxiv.org/abs/hep-th/0610207v1

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62

Sep 20, 2013
09/13

by
Xavier Bekaert; Nicolas Boulanger; Serge Leclercq

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In the eighties, Berends, Burgers and van Dam (BBvD) found a nonabelian cubic vertex for self-interacting massless fields of spin three in flat spacetime. However, they also found that this deformation is inconsistent at higher order for any multiplet of spin-three fields. For arbitrary symmetric gauge fields, we severely constrain the possible nonabelian deformations of the gauge algebra and, using these results, prove that the BBvD obstruction cannot be cured by any means, even by introducing...

Source: http://arxiv.org/abs/1002.0289v1

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39

Sep 20, 2013
09/13

by
Nicolas Boulanger; Nicolo Colombo; Per Sundell

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The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to replacing the classical differential forms by vectorial superfields of fixed total degree given by the sum of form degree and ghost number. The nilpotency of the BRST operator is achieved by imposing boundary conditions and choosing appropriate gauge transitions between charts leading to a...

Source: http://arxiv.org/abs/1205.3339v2

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82

Sep 21, 2013
09/13

by
Xavier Bekaert; Nicolas Boulanger; Sandrine Cnockaert

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We study the problem of consistent interactions for spin-3 gauge fields in flat spacetime of arbitrary dimension n>3. Under the sole assumptions of Poincar\'e and parity invariance, local and perturbative deformation of the free theory, we determine all nontrivial consistent deformations of the abelian gauge algebra and classify the corresponding deformations of the quadratic action, at first order in the deformation parameter. We prove that all such vertices are cubic, contain a total of...

Source: http://arxiv.org/abs/hep-th/0508048v2

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46

Sep 18, 2013
09/13

by
Nicolas Boulanger; Sandrine Cnockaert; Serge Leclercq

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The problem of constructing consistent parity-violating interactions for spin-3 gauge fields is considered in Minkowski space. Under the assumptions of locality, Poincar\'e invariance and parity non-invariance, we classify all the nontrivial perturbative deformations of the abelian gauge algebra. In space-time dimensions $n=3$ and $n=5$, deformations of the free theory are obtained which make the gauge algebra non-abelian and give rise to nontrivial cubic vertices in the Lagrangian, at first...

Source: http://arxiv.org/abs/hep-th/0509118v3

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16

Jun 26, 2018
06/18

by
Xavier Bekaert; Nicolas Boulanger; Dario Francia

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We study the higher-derivative equations for gauge potentials of arbitrary mixed-symmetry type obtained by setting to zero the divergences of the corresponding curvature tensors. We show that they propagate the same reducible multiplets as the Maxwell-like second-order equations for gauge fields subject to constrained gauge transformations. As an additional output of our analysis, we provide a streamlined presentation of the Ricci-like case, where the traces of the same curvature tensors are...

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1501.02462

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6.0

Jun 30, 2018
06/18

by
Thomas Basile; Xavier Bekaert; Nicolas Boulanger

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We prove a generalised 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 $CFT_d$ of fundamental (higher-order) scalar and spinor singletons. As a first check of this conjecture, we...

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1410.7668

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106

Jul 20, 2013
07/13

by
Xavier Bekaert; Nicolas Boulanger; Per Sundell

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Aiming at non-experts, we explain the key mechanisms of higher-spin extensions of ordinary gravity. We first overview various no-go theorems for low-energy scattering of massless particles in flat spacetime. In doing so we dress a dictionary between the S-matrix and the Lagrangian approaches, exhibiting their relative advantages and weaknesses, after which we high-light potential loop-holes for non-trivial massless dynamics. We then review positive yes-go results for non-abelian cubic...

Source: http://arxiv.org/abs/1007.0435v3

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72

Sep 22, 2013
09/13

by
Nicolas Boulanger; Serge Leclercq; Per Sundell

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We address the uniqueness of the minimal couplings between higher-spin fields and gravity. These couplings are cubic vertices built from gauge non-invariant connections that induce non-abelian deformations of the gauge algebra. We show that Fradkin-Vasiliev's cubic 2-s-s vertex, which contains up to 2s-2 derivatives dressed by a cosmological constant $\Lambda$, has a limit where: {(i)} $\Lambda\to 0$; {(ii)} the spin-2 Weyl tensor scales {\emph{non-uniformly}} with s; and {(iii)} all...

Source: http://arxiv.org/abs/0805.2764v2

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86

Sep 22, 2013
09/13

by
Nicolas Boulanger; Carlo Iazeolla; Per Sundell

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Following the general formalism presented in arXiv:0812.3615 -- referred to as Paper I -- we derive the unfolded equations of motion for tensor fields of arbitrary shape and mass in constantly curved backgrounds by radial reduction of Skvortsov's equations in one higher dimension. The complete unfolded system is embedded into a single master field, valued in a tensorial Schur module realized equivalently via either bosonic (symmetric basis) or fermionic (anti-symmetric basis) vector...

Source: http://arxiv.org/abs/0812.4438v2

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117

Sep 23, 2013
09/13

by
Yoshua Bengio; Nicolas Boulanger-Lewandowski; Razvan Pascanu

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After a more than decade-long period of relatively little research activity in the area of recurrent neural networks, several new developments will be reviewed here that have allowed substantial progress both in understanding and in technical solutions towards more efficient training of recurrent networks. These advances have been motivated by and related to the optimization issues surrounding deep learning. Although recurrent networks are extremely powerful in what they can in principle...

Source: http://arxiv.org/abs/1212.0901v2

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56

Sep 22, 2013
09/13

by
Nicolas Boulanger; Marc Henneaux; Peter van Nieuwenhuizen

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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 ${\cal B}^{\mu \nu} = 0$, where ${\cal B}^{\mu \nu}$ 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...

Source: http://arxiv.org/abs/hep-th/0201023v2