Remarks on Higgs Mechanism for Gravitons

We construct two kinds of model exhibiting Higgs mechanism for gravitons in potentials of scalar fields. One class of the model is based on a potential which is a generic function of the induced internal metric $H^{AB}$, and the other involves a potential which is a generic function of the usual metric tensor $g_{μν}$ and the induced curved metric $Y_{μν}$. In the both models, we derive conditions on the scalar potential in such a way that gravitons acquire mass in a flat Minkowski space-time without non-unitary propagating modes in the process of spontaneous symmetry breaking of diffeomorphisms through the condensation of scalar fields. We solve the conditions and find a general solution for the potential. As an interesting specific solution, we present a simple potential for which the Higgs mechanism for gravitons holds in any value of cosmological constant.

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