Topological mass generation and $2-$forms. (arXiv:2003.11736v2 [hep-th] UPDATED)
<a href="http://arxiv.org/find/hep-th/1/au:+Almeida_J/0/1/0/all/0/1">Juan P. Beltrán Almeida</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Guarnizo_A/0/1/0/all/0/1">Alejandro Guarnizo</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Heisenberg_L/0/1/0/all/0/1">Lavinia Heisenberg</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Valenzuela_Toledo_C/0/1/0/all/0/1">César A. Valenzuela-Toledo</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Zosso_J/0/1/0/all/0/1">Jann Zosso</a>
In this work we revisit the topological mass generation of 2-forms and
establish a connection to the unique derivative coupling arising in the quartic
Lagrangian of the systematic construction of massive $2-$form interactions,
relating in this way BF theories to Galileon-like theories of 2-forms. In terms
of a massless $1-$form $A$ and a massless $2-$form $B$, the topological term
manifests itself as the interaction $Bwedge F$, where $F = {rm d} A$ is the
field strength of the $1-$form. Such an interaction leads to a mechanism of
generation of mass, usually referred to as “topological generation of mass” in
which the single degree of freedom propagated by the $2-$form is absorbed by
the $1-$form, generating a massive mode for the $1-$form. Using the
systematical construction in terms of the Levi-Civita tensor, it was shown
that, apart from the quadratic and quartic Lagrangians, Galileon-like
derivative self-interactions for the massive 2-form do not exist. A unique
quartic Lagrangian
$epsilon^{munurhosigma}epsilon^{alphabetagamma}_{;;;;;;sigma}partial_{mu}B_{alpharho}partial_{nu}B_{betagamma}$
arises in this construction in a way that it corresponds to a total derivative
on its own but ceases to be so once an overall general function is introduced.
We show that it exactly corresponds to the same interaction of topological mass
generation. Based on the decoupling limit analysis of the interactions, we
bring out supporting arguments for the uniqueness of such a topological mass
term and absence of the Galileon-like interactions. Finally, we discuss some
preliminary applications in cosmology.
In this work we revisit the topological mass generation of 2-forms and
establish a connection to the unique derivative coupling arising in the quartic
Lagrangian of the systematic construction of massive $2-$form interactions,
relating in this way BF theories to Galileon-like theories of 2-forms. In terms
of a massless $1-$form $A$ and a massless $2-$form $B$, the topological term
manifests itself as the interaction $Bwedge F$, where $F = {rm d} A$ is the
field strength of the $1-$form. Such an interaction leads to a mechanism of
generation of mass, usually referred to as “topological generation of mass” in
which the single degree of freedom propagated by the $2-$form is absorbed by
the $1-$form, generating a massive mode for the $1-$form. Using the
systematical construction in terms of the Levi-Civita tensor, it was shown
that, apart from the quadratic and quartic Lagrangians, Galileon-like
derivative self-interactions for the massive 2-form do not exist. A unique
quartic Lagrangian
$epsilon^{munurhosigma}epsilon^{alphabetagamma}_{;;;;;;sigma}partial_{mu}B_{alpharho}partial_{nu}B_{betagamma}$
arises in this construction in a way that it corresponds to a total derivative
on its own but ceases to be so once an overall general function is introduced.
We show that it exactly corresponds to the same interaction of topological mass
generation. Based on the decoupling limit analysis of the interactions, we
bring out supporting arguments for the uniqueness of such a topological mass
term and absence of the Galileon-like interactions. Finally, we discuss some
preliminary applications in cosmology.
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