Generalization of the 2-form interactions

Abstract

We systematically construct derivative self-interactions for massless and massive 2-forms. There exists a no-go theorem in the literature for constructing Galileon-like Lagrangians in four dimensions for the 2-form with gauge invariance, the Kalb-Rammond field. The presence of non-minimal couplings strongly relies on the contraction with divergenceless tensors. In four dimensions these are the Einstein tensor and the double dual Riemann tensor. Even though they are divergenceless on their own, their combination ceases to be. In the case of massless 2-forms we are not able to establish non-minimal couplings of the 2-form to the gravity sector with second order equations of motion due to the impossibility of building consistent combinations of divergenceless tensors. Using the systematical construction in terms of the Levi-Civita tensor, we aim at constructing Galileon-like derivative self-interactions for the massive 2-form. Apart from $L_2$ and $L_4$ we are not able to construct further Galileon-like Lagrangians. For the massive case, an important non-minimal coupling between the 2-form and the double dual Riemann tensor arises, which receives additional support from the decoupling limit. Promoting the interactions in $L_4$ requires the presence of appropriate non-minimal couplings and we give concrete examples for this.

arXiv comment7 pages, no figures

References in corpus (21)

• 4D Gravity on a Brane in 5D Minkowski Space
• The galileon as a local modification of gravity
• From k-essence to generalised Galileons
• Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
• Generalization of the Proca Action
• A systematic approach to generalisations of General Relativity and their cosmological implications
• Cosmic Acceleration from Abelian Symmetry Breaking
• Derivative self-interactions for a massive vector field
• Arbitrary p-form Galileons
• Cosmology in generalized Proca theories
• Generalized Proca action for an Abelian vector field
• Effective gravitational couplings for cosmological perturbations in generalized Proca theories
• Black holes in vector-tensor theories
• A no-go theorem for generalized vector Galileons on flat spacetime
• A Covariant Master Theory for Novel Galilean Invariant Models and Massive Gravity
• Black Holes and Neutron Stars in Vector Galileons
• The complete theory of Maxwell and Proca fields
• The Maxwell-Proca theory: definition and construction
• On p-form theories with gauge invariant second order field equations
• Generalized Proca and its Constraint Algebra
• 2-form gauge theory dual to scalar-tensor theory

Cited by in corpus (5)

• Gravitational wave memory beyond general relativity
• On the duality of massive Kalb-Ramond and Proca fields
• Topological mass generation and $2-$forms
• Canonical analysis of Kalb-Ramond-Proca duality
• A note on higher rank descriptions of massless and massive spin-1 particles