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Generalization of the 2-form interactions | | Lavinia Heisenberg
; Georg Trenkler
; | | Date: |
25 Aug 2019 | | 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. | | Source: | arXiv, 1908.9328 | | Services: | Forum | Review | PDF | Favorites | |
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