arXiv subjects

D. Dalmazi

Publications and source records attributed to D. Dalmazi.

At least 19 recordsLinked to original sources

arXiv2026

Unitarity of partially broken massless higher-spin models

Here we suggest a partially broken version of the Skvortsov-Vasiliev (SV) model for massless particles of arbitrary integer spin $s\ge 3$. The traceless gauge parameter of the Weyl transformation is now required to be transverse. In the light-cone gauge we offer a simple proof that the model contains only spin-$s$ helicities as propagating modes. In the $s=3$ and $s=4$ cases we are able to calculate the two point amplitude and confirm unitarity in a explicitly Lorentz invariant way. For the recently suggested partially broken Fronsdal model, for $s=3$ and $s=4$, unitarity is also confirmed in a Lorentz invariant way from their two point amplitudes. In both Fronsdal and SV partially broken models the two point amplitudes differ from their unbroken counterparts by contact terms which guarantees the same particle content but indicates potential non-equivalence of possible interacting terms.

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arXiv2026

Linearized transverse diffeomorphism invariant spin-2 theories via gauge invariants

We analyze the particle spectrum of a second-order (in derivatives) theory based on a rank-2 tensor field with both symmetric and antisymmetric components. By demanding the existence of a propagating massless spin-2 particle and invariance under linearized transverse diffeomorphisms, we derive a new class of stable models with two massless scalars and a single massless spin-2 particle. A natural non linear completion is proposed in terms of a dynamical metric field. The identification of the spectrum is carried out using a fully Lagrangian, gauge-invariant approach which makes use of Bardeen variables in a constructive manner. The approach significantly reduces the number of steps in the spectrum determination in some cases.

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arXiv2025

A partially broken Fronsdal model for massless higher-spin particles of integer spin

By introducing arbitrary parameters in the usual Fronsdal model, we find a region in the parameters space away from the ``Fronsdal point'' where we still have an irreducible description of massless particles of arbitrary integer spin $s\ge 3$. The higher spin gauge symmetry is further constrained by a vanishing double divergence condition on the traceless gauge parameter: $\partial\cdot\partial\cdot\barΛ=0$. Remarkably, it does not introduce extra propagating gauge invariants. We demonstrate that we only have spin-$s$ helicity states as propagating modes for arbitrary integer $s\ge 3$. For the simplest $s=3$ case we present a gauge invariant proof while for $s\ge 4$ we use a light-cone gauge. The reduction in the gauge symmetry allows for more general source couplings when compared to the Fronsdal model.

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arXiv2025

Equivalence of spin-2 and spin-3 models invariant under transverse diffeomorphisms and the tensionless limit of string theory

Here we investigate a general class of massless local theories of spin-2 and spin-3 both invariant under generalized transverse diffeomorphisms (TDiff). We identify the ghost free region in their parameters space and show the relationship of those models with the ``doublet'' action stemming from the tensionless limit of the open bosonic string field theory (for symmetric tensors). The connection is implemented via a non local field redefinition which introduces a Stuckelberg-like field of rank-0 (rank-1) for the spin-2 (spin-3) case. An apparent mismatch between most of the TDiff models and the ``doublet'' action has led us to prove a nontrivial duality within the TDiff models which restores the equivalence. Any point in the parameters subspace of ghost free TDiff models is equivalent to any other one within that subspace. In particular, they are all physically equivalent to their simplest version known as Maxwell-like models. So the physical TDiff models seem to differ from each other by a BRST cohomologically trivial term.

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arXiv2025

More on unconstrained descriptions of Higher Spin Massless Particles

Here we suggest a new local action describing arbitrary integer spin-$s$ massless particles in terms of only two symmetric fields $φ$ and $α$ of rank-$s$ and $(s-3)$ respectively. It is an unconstrained version of the Fronsdal theory where the double traceless constraint on the physical field is evaded via a rank-$(s-4)$ Weyl like symmetry. The constrained higher spin diffeomorphism is enlarged to full diffeomorphism via the Stueckelberg field $α$ through an appropriate field redefinition. After a partial gauge fixing where the Weyl symmetry is broken while preserving diffeomorphisms, the field equations reproduce, for arbitrary integer spin-$s$, diffeomorphism invariant equations of motion previously obtained via a truncation of the spectrum of the open bosonic string field theory in the tensionless limit. In the $s=4$ case we show that the functional integration over $α$ leads to a unique non local Weyl and diffeomorphism invariant action given only in terms of the physical field $φ$ whose spectrum is confirmed via an analysis of the analytic structure of the spin-4 propagator for which we introduce a complete basis of projection and transition non local differential operators. We also show that the elimination of $α$ after the Weyl gauge fixing leads to a non local diffeomorphism invariant action previously obtained in the literature.

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arXiv2024

Generators of the Poincaré Group for arbitrary tensors and spinor-tensors

In this work, we systematically derive explicit expressions for the Poincaré Group generators on arbitrary-rank tensors and spinor-tensors in $D=3+1$ and $D=2+1$ spacetimes, thus generalizing previous works in the literature for the groups $ISO(3,1)$ and $ISO(2,1)$. From the Casimir eigenvalue equations, we demonstrate in a model-independent way the Fierz-Pauli constraints for massive particles for spins $\mathfrak{s}=5/2$, 3, and 4 in $D=3+1$ and helicities $α=5/2$, 3, and 4 in $D=2+1$ dimensions. We also comment on the demonstration of the Fierz-Pauli constraints for the general case of arbitrary spin (helicity).

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arXiv2023

More on the spin-2 analogue of the massive BF model

The addition of mass terms in general breaks gauge symmetries which can be recovered usually via Stueckelberg fields. The massive BF model describes massive spin-1 particles while preserving the $U(1)$ symmetry without Stueckelberg fields. Replacing the spin-1 curvature (field strength) by the Riemann tensor one can define its spin-2 analogue (massive``BR'' model). Here we investigate the canonical structure of the free mBR model in terms of gauge invariants in arbitrary dimensions and compare with the massive BF model. We also investigate non linear completions of the mBR model in arbitrary dimensions. In $D=3$ we find a non linear completion in the form of a bimetric model which is a sub case of a new class of bimetric models whose decoupling limit is ghost free at leading order. Their spectrum consists only of massive spin-2 particles. In arbitrary dimensions $D\ge 3$ we show that the consistency of a possible single metric completion of the mBR model is related with the consistency of a higher rank description of massless spin-1 particles in arbitrary backgrounds.

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arXiv2022

A note on higher rank descriptions of massless and massive spin-1 particles

The Maxwell theory can be written as a first order model with the help of a two-form auxiliary field, such master action allows the proof of duality between $1$-form and $D-3$ forms. Here we show that the replacement of the two-form auxiliary field by an arbitrary (non symmetric) rank-2 tensor leads to a new massless spin-1 dual theory in terms of a partially antisymmetric rank-3 tensor. In the massive spin-1 case we have a non symmetric generalization of the massive two-form theory (Kalb-Ramond). The coupling of the massive non symmetric spin-1 model to matter fields is investigated via master actions. We also show that massive models with severe discontinuity in their massless limit can also be obtained from Kaluza-Klein dimensional reduction of massless higher rank tensors which become Stueckelberg fields after the reduction.

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arXiv2021

Self-dual models in $D=2+1$ from dimensional reduction

Here we perform a Kaluza-Klein dimensional reduction of Vasiliev's first-order description of massless spin-s particles from $D=3+1$ to $D=2+1$ and derive first-order self-dual models describing particles with helicities $\pm s$ for the cases $s=1,2,3$. In the first two cases we recover known (parity singlets) self-dual models. In the spin-3 case we derive a new first order self-dual model with a local Weyl symmetry which lifts the traceless restriction on the rank-3 tensor. A gauge fixed version of this model corresponds to a known spin-3 self-dual model. We conjecture that our procedure can be generalized to arbitrary integer spins.

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arXiv2021

On higher spin analogues of linearized Topologically Massive Gravity and linearized "New Massive Gravity"

We suggest a new spin-4 self-dual model (parity singlet) and a new spin-4 parity doublet in $D=2+1$. They are of higher order in derivatives and are described by a totally symmetric rank-4 tensor without extra auxiliary fields. Despite the higher derivatives they are ghost free. We find gauge invariant field combinations which allow us to show that the canonical structure of the spin-4 (spin-3) models follows the same pattern of its spin-2 (spin-1) counterpart after field redefinitions. For $s=1,2,3,4$, the spin-$s$ self-dual models of order $2s-1$ and the doublet models of order $2s$ can be written in terms of three gauge invariants. The cases $s=3$ and $s=4$ suggest a restricted conformal higher spin symmetry as a principle for defining linearized topologically massive gravity and linearized "New Massive Gravity" for arbitrary integer spins. A key role in our approach is played by the fact that the Cotton tensor in $D=2+1$ has only two independent components for any integer spin.

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arXiv2021

The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms

Here we perform the Kaluza-Klein dimensional reduction from $D+1$ to $D$ dimensions of massless Lagrangians described by a symmetric rank-2 tensor and invariant under transverse differmorphisms (TDiff). They include the linearized Einstein-Hilbert theory, linearized unimodular gravity and scalar tensor models. We obtain simple expressions in terms of gauge invariant field combinations and show that unitarity is preserved in all cases. After fixing a gauge, the reduced model becomes a massive scalar tensor theory. We show that the diffeomorphism (Diff) symmetry, instead of TDiff, is a general feature of the massless sector of consistent massive scalar tensor models. We discuss some subtleties when eliminating Stückelberg fields directly at action level as gauge conditions. We also show that the reduced models all have a smooth massless limit. A non local connection between the massless sector of the scalar tensor theory and the pure tensor TDiff model leads to a parametrization of the non conserved source which naturally separates spin-0 and spin-2 contributions in the pure tensor theory. The case of curved backgrounds is also investigated. If we truncate the non minimal couplings to linear terms in the curvature, vector and scalar constraints require Einstein spaces as in the Diff and WTDiff (Weyl plus Diff) cases. We prove that our linearized massive scalar tensor models admit those curved background extensions.

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arXiv2020

More on dual actions for massive spin-2 particles

Here we start from a dual version of Vasiliev's first order action for massless spin-2 particles (linearized first order Einstein-Hilbert) and derive, via Kaluza-Klein dimensional reduction from $D+1$ to $D$ dimensions, a set of dual massive spin-2 models. This set includes the massive "BR" model, a spin-2 analogue of the spin-1 Cremmer-Scherk model. In our approach the linearized Riemann curvature emerges from a solution of a functional constraint. In $D=2+1$ the BR model can be written as a linearized version of a new bimetric model for massive gravitons. We also have a new massive spin-2 model, in arbitrary dimensions, invariant under linearized diffeomorphisms. It is given in terms of a non symmetric rank-2 tensor and a mixed symmetry tensor.

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arXiv2019

Soldering spin-3 opposite helicities in $D=2+1$

Here we present the `soldering' of opposite helicity states of a spin-3 particle, in $D=2+1$, into one parity doublet. The starting points may be either the sixth- or the fifth-order (in derivatives) spin-3 self-dual models of opposite helicities. The high number of derivatives avoids the use of auxiliary fields which has been so far an obstacle for a successful soldering procedure. The resulting doublet model is a new Lagrangian with six orders in derivatives and no auxiliary field. It may be regarded as a spin-3 analogue of the linearized `New Massive Gravity'. We check its particle content via a gauge invariant and Lorentz covariant analysis of the analytic structure of the two-point amplitude with the help of spin-3 analogues of the Barnes and Rivers projection operators. The particle content is alternatively confirmed in a specific non-covariant gauge by a decomposition in helicity variables. The soldered model is ghost free and contains two physical states as expected for a parity doublet.

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arXiv2019

Parity singlets and doublets of massive spin-3 particles in $D=2+1$ via Nother gauge embedding

Here we demonstrate that the sixth order (in derivatives) spin-3 self-dual model can be obtained from the fifth order self-dual model via a Noether Gauge Embedding (NGE) of longitudinal Weyl transformations $η_{(μν}\partial_{α)}Φ$. In the case of doublet models we can show that the massive spin-3 Singh-Hagen theory is dual to a fourth and to a sixth order theory, via a double round of the NGE procedure by imposing traceless longitudinal (reparametrization-like) symmetries $\partial_{(μ}\tildeξ_{να)}$ in the first round and transverse Weyl transformations $η_{(μν}ψ^T_{α)}$ in the second one. Our procedure automatically furnishes the dual maps between the corresponding fields.

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arXiv2019

Unimodular gravity theory with external sources in a Lorentz-symmetry breaking scenario

This paper is dedicated to the study of interactions between stationary field sources for the linearized unimodular gravity or WTDIFF theory in a model which exhibits Lorentz symmetry breaking due to the presence of the linearized topological Chern-Simons term in $3 + 1$ dimensions, where the Lorentz symmetry breaking is caused by a single background vector $v^μ$. Since the background vector is very tiny, we treat it perturbatively up to second order and we focus on physical phenomena which have no counterpart in standard WTDIFF theory. We consider effects related to field sources describing point-like particles and cosmic strings. We show that in a Lorentz violating scenario the interaction between external sources lead to numerically different results for linerarized Eintein-Hilbert (LEH) and WTDIFF theories, however both results are qualitatively similar and can be equalized after a rescaling of the Lorentz breaking source term which makes an experimental distinction impossible at leading order in pertubation theory as far as point particles and cosmic strings are concerned.

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arXiv2019

Note on massless and partially massless spin-2 particles in a curved background via a nonsymmetric tensor

In the last few years we have seen an increase interest on gravitational waves due to recent and striking experimental results confirming Einstein's general relativity once more. From the field theory point of view, gravity describes the propagation of self-interacting massless spin-2 particles. They can be identified with metric perturbations about a given background metric. Since the metric is a symmetric tensor, the massless spin-2 particles present in the Einstein-Hilbert (massless Fierz-Pauli) theory are naturally described by a symmetric rank-2 tensor. However, this is not the only possible consistent massless spin-2 theory at linearized level. In particular, if we add a mass term, a new one parameter $(a_1)$ family of models ${\cal L}(a_1)$ shows up. They consistently describe massive spin-2 particles about Einstein spaces in terms of a non-symmetric rank-2 tensor. Here we investigate the massless version of ${\cal L}(a_1)$ in a curved background. In the case $a_1=-1/12$ we show that the massless spin-2 particles consistently propagate, at linearized level, in maximally symmetric spaces. A similar result is obtained otherwise $(a_1 \ne -1/12)$ where we have a non-symmetric scalar-tensor massless model. The case of partially massless non-symmetric models is also investigated.

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arXiv2018

Higher order self-dual models for spin-3 particles in $D=2+1$

In $D=2+1$ dimensions, elementary particles of a given helicity can be described by local Lagrangians (parity singlets). By means of a "soldering" procedure two opposite helicities can be joined together and give rise to massive spin-$s$ particles carrying both helicities $\pm s$ (parity doublets), such Lagrangians can also be used in $D=3+1$ to describe massive spin-$s$ particles. From this point of view the parity singlets (self-dual models) in $D=2+1$ are the building blocks of real massive elementary particles in $D=3+1$. In the three cases $s=1,\, 3/2,\, 2$ there are $2s$ self-dual models of order $1,2, \cdots, 2s$ in derivatives. In the spin-3 case the 5th order model is missing in the literature. Here we deduce a 5th order spin-3 self-dual model and fill up this gap. It is shown to be ghost free by means of a master action which relates it with the top model of 6th order. We believe that our approach can be generalized to arbitrary integer spin-$s$ in order to obtain the models of order $2s$ and $2s-1$. We also comment on the difficulties in relating the 5th order model with their lower order duals.

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arXiv2017

Weyl and transverse diffeomorphism invariant spin-2 models in D=2+1

There are two covariant descriptions of massless spin-2 particles in $D=3+1$ via a symmetric rank-2 tensor: the linearized Einstein-Hilbert (LEH) theory and the Weyl plus transverse diffeomorphism (WTDIFF) invariant model. From the LEH theory one can obtain the linearized New Massive Gravity (NMG) in $D=2+1$ via Kaluza-Klein dimensional reduction followed by a dual master action. Here we show that a similar route takes us from the WTDIFF model to a linearized scalar tensor NMG which belongs to a larger class of consistent spin-0 modifications of NMG. We also show that a traceless master action applied to a parity singlet furnishes two new spin-2 selfdual models. Moreover, we examine the singular replacement $h_{μν} \to h_{μν} - η_{μν}h/D$ and prove that it leads to consistent massive spin-2 models in $D=2+1$. They include linearized versions of unimodular topologically massive gravity (TMG) and unimodular NMG. Although the free part of those unimodular theories are Weyl invariant, we do not expect any improvement in the renormalizability. Both the linearized K-term (in NMG) and the linearized gravitational Chern-Simons term (in TMG) are invariant under longitudinal reparametrizations $δh_{μν} = \p_μ\p_νζ$ which is not a symmetry of the WTDIFF Einstein-Hilbert term. Therefore, we still have one degree of freedom whose propagator behaves like $1/p^2$ for large momentum.

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