Abstract

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 $B\wedge F$, 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 $\epsilon^{\mu\nu\rho\sigma}\epsilon^{\alpha\beta\gamma}_{\;\;\;\;\;\;\sigma}\partial_{\mu}B_{\alpha\rho}\partial_{\nu}B_{\beta\gamma}$ 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.

Highlights

  • The successful construction of Galileon theories [1] has changed our perspective on standard effective field theories (EFTs)

  • 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

  • The construction of effective field theories is straightforward after determining the involved symmetries and the field content

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Summary

INTRODUCTION

The successful construction of Galileon theories [1] has changed our perspective on standard effective field theories (EFTs). Derivatives acting on the field strength of a Maxwell field do not permit the construction of Lagrangians with second-order equations of motion and gauge invariance. This obstruction does not apply to the case of massive spin-1 fields. The authors discussed general models of interacting p-form Lagrangians subject to the following restrictions: 1) Uð1Þ gauge invariance, 2) up to first order derivatives of the p-forms in the Lagrangian, 3) up to cubic terms in the derivatives of the p-forms, 4) having a Hamiltonian bounded from below, and 5) hyperbolicity of the equations of motion [29]. The term B ∧ F [21,22,23] is responsible for the mechanism of topological generation of mass described in detail in Refs. [24,25,26]

Relating BF with Galileon-like interactions
Including the duals in the systematic construction
SYSTEMATICAL CONSTRUCTION
DECOUPLING LIMIT ANALYSIS
FIRST COSMOLOGICAL APPLICATION
Gauge invariant
Nonminimal coupling
CONCLUSION
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