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Serge Leclercq

Publications and source records attributed to Serge Leclercq.

7 recordsLinked to original sources
arXiv2010

Higher spin interactions: cubic deformations on Minkowski and (Anti)de Sitter backgrounds

In the thesis, results presented in various papers involving the author are reviewed. First, general results about consistent deformations at first order (i.e. cubic) using the antifield formalism in Minkowski spacetime are gathered. Secondly, a correspondance between the consistent nonabelian cubic vertices in (Anti)de Sitter and those in Minkowski spacetime is establish. The Minkowski nonabelian cubic solutions for the triplets of spin 2-2-3, 3-3-3 (in particular the parity-breaking ones), 1-s-s and 2-s-s are then studied, the last of which providing the uniqueness of the 2-s-s Fradkin-Vasiliev deformation procedure in (A)dS spacetime. Finally, we carry out second order computations in Minkowski spacetime that show the inconsistency of several cubic solutions, including the spin-3 Berends-Burgers-van Dam vertex.

hep-th↗
arXiv2010

Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex

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 fields of spin higher (or lower) than three.

hep-th↗
arXiv2008

On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory

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 $Λ$, has a limit where: {(i)} $Λ\to 0$; {(ii)} the spin-2 Weyl tensor scales {\emph{non-uniformly}} with s; and {(iii)} all lower-derivative couplings are scaled away. For s=3 the limit yields the unique non-abelian spin 2-3-3 vertex found recently by two of the authors, thereby proving the \emph{uniqueness} of the corresponding FV vertex. We extend the analysis to s=4 and a class of spin 1-s-s vertices. The non-universality of the flat limit high-lightens not only the problematic aspects of higher-spin interactions with $Λ=0$ but also the strongly coupled nature of the derivative expansion of the fully nonlinear higher-spin field equations with $Ł\neq 0$, wherein the standard minimal couplings mediated via the Lorentz connection are \emph{subleading} at energy scales $\sqrt{|Λ|}<< E<< M_{\rm p}$. Finally, combining our results with those obtained by Metsaev, we give the complete list of \emph{all} the manifestly covariant cubic couplings of the form 1-s-s and 2-s-s, in Minkowski background.

hep-th↗
arXiv2006

Consistent couplings between spin-2 and spin-3 massless fields

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.

hep-th↗
arXiv2006

Parity violating vertices for spin-3 gauge fields

The problem of constructing consistent parity-violating interactions for spin-3 gauge fields is considered in Minkowski space. Under the assumptions of locality, Poincaré 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 order in the deformation parameter $g$. At second order in $g$, consistency conditions are obtained which the five-dimensional vertex obeys, but which rule out the $n=3$ candidate. Moreover, in the five-dimensional first order deformation case, the gauge transformations are modified by a new term which involves the second de Wit--Freedman connection in a simple and suggestive way.

hep-th↗
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↗