Higgs Mechanism for Gravitons

TL;DR

This paper explores the gravitational Higgs mechanism, demonstrating how gravitons can acquire mass through scalar field condensation without non-unitary modes, and identifies conditions for such mechanisms in various models.

Contribution

It generalizes existing models of gravitational Higgs mechanism, identifying new potential classes and clarifying conditions for ghost mode decoupling in diverse space-time dimensions.

Findings

Identified two classes of potentials exhibiting gravitational Higgs mechanism.

Generalized the model to include arbitrary potentials.

Clarified conditions for ghost mode decoupling in various dimensions.

Abstract

Just like the vector gauge bosons in the gauge theories, it is now known that gravitons acquire mass in the process of spontaneous symmetry breaking of diffeomorphisms through the condensation of scalar fields. The point is that we should find the gravitational Higgs mechanism such that it results in massive gravity in a flat Minkowski space-time without non-unitary propagating modes. This is usually achieved by including higher-derivative terms in scalars and tuning the cosmological constant to be a negative value in a proper way. Recently, a similar but different gravitational Higgs mechanism has been advocated by Chamseddine and Mukhanov where one can relax the negative cosmological constant to zero or positive one. In this work, we investigate why the non-unitary ghost mode decouples from physical Hilbert space in a general space-time dimension. Moreover, we generalize the model to possess an arbitrary potential and clarify under what conditions the general model exhibits the gravitational Higgs mechanism. By searching for solutions to the conditions, we arrive at two classes of potentials exhibiting gravitational Higgs mechanism. One class includes the model by Chamseddine and Mukhanov in a specific case while the other is completely a new model.