arXiv subjects

Nicolas Boulanger

Publications and source records attributed to Nicolas Boulanger.

At least 37 records · Page 2Linked to original sources

arXiv2021

Note on the bundle geometry of field space, variational connections, the dressing field method, & presymplectic structures of gauge theories over bounded regions

In this note, we consider how the bundle geometry of field space interplays with the covariant phase space methods so as to allow to write results of some generality on the presymplectic structure of invariant gauge theories coupled to matter. We obtain in particular the generic form of Noether charges associated with field-independent and field-dependent gauge parameters, as well as their Poisson bracket. We also provide the general field-dependent gauge transformations of the presymplectic potential and 2-form, which clearly highlight the problem posed by boundaries in generic situations. We then conduct a comparative analysis of two strategies recently considered to evade the boundary problem and associate a modified symplectic structure to a gauge theory over a bounded regions: namely the use of edge modes on the one hand, and of variational connections on the other. To do so, we first try to give the clearest geometric account of both, showing in particular that edge modes are a special case of differential geometric tool of gauge symmetry reduction known as the "dressing field method". Applications to Yang-Mills theory and General Relativity reproduce or generalise several results of the recent literature.

math-ph↗

arXiv2021

The unitary representations of the Poincare group in any spacetime dimension

An extensive group-theoretical treatment of linear relativistic field 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 field 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 of the stability subgroups only. Therefore, an exhaustive treatment of the two most important classes of unitary irreducible representations, corresponding to massive and massless particles (the latter class decomposing in turn into the ``helicity'' and the "infinite-spin" representations) may be performed via the well-known representation theory of the orthogonal groups O(n) (with D-4<n<D). Finally, covariant field equations are given for each unitary irreducible representation of the Poincare group with non-negative mass-squared. Tachyonic representations are also examined. All these steps are covered in many details and with examples. The present notes also include a self-contained review of the representation theory of the general linear and (in)homogeneous orthogonal groups in terms of Young diagrams.

hep-th↗

arXiv2021

Higher spins from exotic dualisations

At the free level, a given massless field can be described by an infinite number of different potentials related to each other by dualities. In terms of Young tableaux, dualities replace any number of columns of height $h_i$ by columns of height $D-2-h_i$, where $D$ is the spacetime dimension: in particular, applying this operation to empty columns gives rise to potentials containing an arbitrary number of groups of $D-2$ extra antisymmetric indices. Using the method of parent actions, action principles including these potentials, but also extra fields, can be derived from the usual ones. In this paper, we revisit this off-shell duality and clarify the counting of degrees of freedom and the role of the extra fields. Among others, we consider the examples of the double dual graviton in $D=5$ and two cases, one topological and one dynamical, of exotic dualities leading to spin three fields in $D=3$.

hep-th↗

arXiv2020

A theory for multiple partially massless spin-2 fields

We revisit the problem of building consistent interactions for a multiplet of partially massless spin-2 fields in (anti-)de Sitter space. After rederiving and strengthening the existing no-go result on the impossibility of Yang-Mills type non-abelian deformations of the partially massless gauge algebra, we prove the uniqueness of the cubic interaction vertex and field-dependent gauge transformation that generalize the structures known from single-field analyses and in four spacetime dimensions, where our results also hold. Unlike in the case of one partially massless field, however, we show that for two or more particle species the cubic deformations can be made consistent at the complete non-linear level, albeit at the expense of allowing for negative relative signs between kinetic terms, making our new theory akin to conformal gravity. Our construction thus provides the first example of an interacting theory containing only partially massless fields.

hep-th↗

arXiv2019

Mixed-symmetry fields in de Sitter space: a group theoretical glance

We rederive the characters of all unitary irreducible representations of the $(d+1)$-dimensional de Sitter spacetime isometry algebra $\mathfrak{so}(1,d+1)$, 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 comment on a possible equivalent of the scalar singleton for the de Sitter (dS) spacetime.

hep-th↗

arXiv2019

Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants

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.

physics.class-ph↗

arXiv2018

Uniqueness of $\mathcal{N}=2$ and $3$ pure supergravities in 4D

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 ${\cal N}=2$ 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, ${\cal N}$ real spin-3/2 gauge fields and at most one real spinor field also requires gravity and yields ${\cal N}=3$ pure supergravity as well as ${\cal N}=1$ pure supergravity coupled to a vector supermultiplet, with or without cosmological terms. Independently from 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.

hep-th↗

arXiv2018

Spin-2 twisted duality in (A)dS

Starting from the dual Lagrangians recently obtained for (partially) massless spin-2 fields in the Stueckelberg formulation, we write the equations of motion for (partially) massless gravitons in (A)dS in the form of twisted-duality relations. In both cases, the latter admit a smooth flat limit. In the massless case, this limit reproduces the gravitational twisted-duality relations previously known for Minkowski spacetime. In the partially-massless case, our twisted-duality relations preserve the number of degrees of freedom in the flat limit, in the sense that they split into a decoupled pair of dualities for spin-1 and spin-2 fields. Our results apply to spacetimes of any dimension greater than three. In four dimensions, the twisted-duality relations for partially massless fields that appeared in the literature are recovered by gauging away the Stueckelberg field.

hep-th↗

arXiv2018

A classification of global conformal invariants

We provide the full classification, in arbitrary even and odd dimensions, of global conformal invariants, i.e., scalar densities in the spacetime metric and its derivatives that are invariant, possibly up to a total derivative, under local Weyl rescalings of the metric. We use cohomological techniques that have already proved instrumental in the classification of Weyl anomalies in arbitrary dimensions. The approach we follow is purely algebraic and borrows techniques originating from perturbative Quantum Field Theory for which locality is crucial.

math-ph↗

arXiv2018

Dual actions for massless, partially-massless and massive gravitons in (A)dS

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 partially-massless 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.

hep-th↗

arXiv2018

Consistent deformations of free massive field theories in the Stueckelberg formulation

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.

hep-th↗

arXiv2018

Deformations of vector-scalar models

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.

hep-th↗

arXiv2018

A note on local BRST cohomology of Yang-Mills type theories with free abelian factors

We extend previous work on antifield dependent local BRST cohomology for matter coupled gauge theories of Yang-Mills type to the case of gauge groups that involve free abelian factors. More precisely, we first investigate in a model independent way how the dynamics enters the computation of the cohomology for a general class of Lagrangians in general spacetime dimensions. We then discuss explicit solutions in the case of specific models. Our analysis has implications for the structure of characteristic cohomology and for consistent deformations of the classical models, as well as for divergences/counterterms and for gauge anomalies that may appear during perturbative quantization.

hep-th↗

arXiv2017

Noncommutative Wilson lines in higher-spin theory and correlation functions of conserved currents for free conformal fields

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 higher-spin 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.

hep-th↗

arXiv2017

The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields

A first-order differential equation is provided for a one-form, spin-s connection valued in the two-row, width-(s-1) Young tableau of GL(5). The connection is glued to a zero-form identified with the spin-s Cotton tensor. The usual zero-Cotton equation for a symmetric, conformal spin-s tensor gauge field in 3D is the flatness condition for the sum of the GL(5) spin-s and background connections. This presentation of the equations allows to reformulate in a compact way the cohomological problem studied in 1511.07389, featuring the spin-s Schouten tensor. We provide full computational details for spin 3 and 4 and present the general spin-s case in a compact way.

hep-th↗

arXiv2016

Frobenius-Chern-Simons gauge theory

Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H, we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an Z_2-graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in arXiv:1505.04957 as an off-shell formulation of the minimal bosonic four-dimensional higher spin gravity theory. If F is unital and the Z_2-grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in the direct product of H and F. We give a new model of this type based on a twisting of C[Z_2 x Z_4], which leads to self-dual complexified gauge fields on AdS_4. If F is 3-graded, the FCS model can be truncated consistently as to zero-form constraints on-shell. Two examples thereof are a twisting of C[(Z_2)^3] that yields the original model, and the Clifford algebra Cl_2n which provides an FCS formulation of the bosonic Konstein--Vasiliev model with gauge algebra hu(4^{n-1},0).

hep-th↗

arXiv2016

Structure constants of shs$[λ]$: the deformed-oscillator point of view

We derive and spell out the structure constants of the $\mathbb{Z}_2$-graded algebra $\mathfrak{shs}[λ]\,$ by using deformed-oscillators techniques in $Aq(2;ν)\,$, 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 Vasiliev in order to construct the higher spin algebras in three spacetime dimensions. We derive an expression for the structure constants of $\mathfrak{shs}[λ]\,$ and show that they must obey a recurrence relation as a consequence of the associativity of the star product. We solve this condition and show that the $\mathfrak{hs}[λ]\,$ structure constants are given by those postulated by Pope, Romans and Shen for the Lone Star product.

hep-th↗

arXiv2016

4D Higher Spin Gravity with Dynamical Two-Form as a Frobenius--Chern--Simons Gauge Theory

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 algebra and a higher spin algebra extended by inner Klein operators. The superconnection consists of two one-forms gauging the one-sided actions of the higher spin algebra, two bi-fundamental real forms given by the Weyl zero-form and a new dynamical two-form, an additional set of forms providing a maximal duality extension, and, finally, the Lagrange multipliers required for the covariant Hamiltonian action. In a particular two-form background, the model yields Vasiliev's recently proposed extended higher spin gravity equations, whose interaction terms are accounted for by de Rham closed globally defined forms arising in the dynamical two-form.

hep-th↗