Gravitational Higgs Mechanism with a Topological Term

Understand

We investigate the Higgs mechanism for gravity, which has been recently put forward by 't Hooft, when the Polyakov-type action for scalar fields is added to the original action.

• We find that from the Polyakov-type action, it is very natural to derive an 'alternative' metric tensor composed of the scalar fields.
• The positivity condition on the determinant can be also derived easily by requiring that this term does not change the dynamics at all and becomes a topological number, that is, the wrapping number.
• It turns out that the gauge conditions adopted by 't Hooft are nothing but the restriction on a sector with unit wrapping number.