2d gravity stress tensor and the problem of the calculation of the multi-loop amplitudes in the string theory
arXiv:hep-th/9411032 · doi:10.1016/0370-2693(94)01374-L
Abstract
It is shown that the vacuum value of the gravity stress tensor in the free field theory is singular in the fundamental region on the complex plane where the genus- Riemann surface 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 gravity field that turns out to be on the genus- Riemann surfaces.
13 pages, LATEX, November 1994