  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.
