Spontaneous compactification in 2D induced quantum gravity

Spontaneous compactification ---on a $R^1\times S^1$ background--- in 2D induced quantum gravity (considered as a toy model for more fundamental quantum gravity) is analyzed in the gauge-independent effective action formalism. It is shown that such compactification is stable, in contradistinction to multidimensional quantum gravity on a $R^D\times S^1 \ (D>2)$ background ---which is known to be one-loop unstable.