Abstract :
It is shown that the vacuum value of the 2D gravity stress tensor in the free field theory is singular in the fundamental region on the complex plane where the genus-n > 1 Riemann surfaces are mapped. Because of the above singularity, one can not construct modular invariant multi-loop amplitudes. The discussed singularity is due to the singularity in the vacuum value of the 2D gravity field that turns out to be on the genus-n > 1 Riemann surfaces.
