arXiv subjects

Elias L. Mendonça

Publications and source records attributed to Elias L. Mendonça.

4 recordsLinked to original sources

arXiv2024

Master Actions and Helicity Decomposition for Spin-4 Models in $3D$

The present work introduces a master action that interpolates between four self-dual models, $SD(i)$, for describing massive spin-4 particles in $D=2+1$ dimensions. These models are designated by $i=1,2,3$ and $4$, representing the order in derivatives. Our results show that the four descriptions are quantum equivalent through comparison of their correlation functions, up to contact terms. A geometrical approach is demonstrated to be a useful tool in describing the third and fourth order models. The construction of the master action relies on the introduction of mixing terms, which must be free of particle content. We use the helicity decomposition method to verify the absence of particle content in these terms, ensuring the proper functioning of the master action.

hep-th↗

arXiv2021

Reaching out a "geometrical" description for spin-4 self-dual models in $D=2+1$

Starting with a first order in derivatives self-dual model which describes a massive spin-4 mode in $D=2+1$ dimensions, we have obtained a sequence of three more new descriptions, which then give us an interconnected self-dual chain $SD(i)$ with $i=1,2,3,4$ indicating the order in derivatives. We have demonstrated that a powerful notation in terms of a self-adjoint operator $Ω$ in the frame-like scenario truly simplifies the investigation for new models and at the third order level can be converted to a geometrical description in terms of the much more usual totally symmetric double traceless field.

hep-th↗

arXiv2010

Duality of parity doublets of helicity $\pm 2$ in $D=2+1$

In $D=2+1$ dimensions there are two dual descriptions of parity singlets of helicity $\pm 1$, namely the self-dual model of first-order (in derivatives) and the Maxwell-Chern-Simons theory of second-order. Correspondingly, for helicity $\pm 2$ there are four models $S_{SD\pm}^{(r)}$ describing parity singlets of helicities $\pm 2$. They are of first-, second-,third- and fourth-order ($r=1,2,3,4$) respectively. Here we show that the generalized soldering of the opposite helicity models $S_{SD+}^{(4)}$ and $S_{SD-}^{(4)}$ leads to the linearized form of the new massive gravity suggested by Bergshoeff, Hohm and Townsend (BHT) similarly to the soldering of $S_{SD+}^{(3)}$ and $S_{SD-}^{(3)}$. We argue why in both cases we have the same result. We also find out a triple master action which interpolates between the three dual models: linearized BHT theory, $S_{SD+}^{(3)} + S_{SD-}^{(3)}$ and $S_{SD+}^{(4)} + S_{SD-}^{(4)}$. By comparing gauge invariant correlation functions we deduce dual maps between those models. In particular, we learn how to decompose the field of the linearized BHT theory in helicity eigenstates of the dual models up to gauge transformations.

hep-th↗

arXiv2009

Generalized soldering of $\pm 2$ helicity states in $D=2+1$

The direct sum of a couple of Maxwell-Chern-Simons (MCS) gauge theories of opposite helicities $\pm 1$ does not lead to a Proca theory in $D=2+1$, although both theories share the same spectrum. However, it is known that by adding an interference term between both helicities we can join the complementary pieces together and obtain the physically expected result. A generalized soldering procedure can be defined to generate the missing interference term. Here we show that the same procedure can be applied to join together $\pm 2$ helicity states in a full off-shell manner. In particular, by using second-order (in derivatives) self-dual models of helicities $\pm 2$ (spin two analogues of MCS models) the Fierz-Pauli theory is obtained after soldering. Remarkably, if we replace the second-order models by third-order self-dual models (linearized topologically massive gravity) of opposite helicities we end up after soldering exactly with the new massive gravity theory of Bergshoeff, Hohm and Townsend in its linearized approximation.

hep-th↗