Classifying Galileon $p$-form theories

Abstract

We provide a complete classification of all abelian gauge invariant $p$-form theories with equations of motion depending only on the second derivative of the field---the $p$-form analogues of the Galileon scalar field theory. We construct explicitly the nontrivial actions that exist for spacetime dimension $D\le 11$, but our methods are general enough and can be extended to arbitrary $D$. We uncover in particular a new $4$-form Galileon cubic theory in $D\ge 8$ dimensions. As a by-product we give a simple proof of the fact that the equations of motion depend on the $p$-form gauge fields only through their field strengths, and show this explicitly for the recently discovered $3$-form Galileon quartic theory.

17 pages; v2: references added

References in corpus (15)

• Covariant Galileon
• Healthy theories beyond Horndeski
• Multi-field galileons and higher co-dimension branes
• Symmetries for Galileons and DBI scalars on curved space
• Bi-galileon theory I: motivation and formulation
• Galileons as Wess-Zumino Terms
• Hamiltonian structure of scalar-tensor theories beyond Horndeski
• Multi-galileons, solitons and Derrick's theorem
• Generalized Galileon Duality
• Generalized SU(2) Proca Theory
• Generalized multi-Proca fields
• Geometry of Special Galileon
• New terms for scalar multi-Galileon models and application to SO(N) and SU(N) group representations
• Tensor Galileons and Gravity
• Spontaneous "Scalar-Vector Galileons" from "Weyl bi-Connection" model

Cited by in corpus (13)

• A systematic approach to generalisations of General Relativity and their cosmological implications
• New Weyl-invariant vector-tensor theory for the cosmological constant
• New class of Proca interactions
• Arbitrarily coupled $p-$forms in cosmological backgrounds
• Anisotropic inflation with coupled $\mathbf{p}$-forms
• Galileon intermediate inflation
• Gauged Galileons
• Towards the extended SU(2) Proca theory
• A unified approach to standard and exotic dualizations through graded geometry
• Shift Symmetries for p-Forms and Mixed Symmetry Fields on (A)dS
• Galileon-like vector fields
• Ghost-free scalar-fermion interactions
• Tensor Galileons as Lovelock theories