2d gravity stress tensor and the problem of the calculation of the multi-loop amplitudes in the string theory

Details 2d gravity stress tensor and the problem of the calculation of the multi-loop amplitudes in the string theory 2d gravity stress tensor and the problem of the calculation of the multi-loop amplitudes in the string theory

1994-11-04

arxiv.org/abs/hep-th/9411032v1

Phys. Lett. B342 (1995) 73-78

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, LATEX, November 1994

Scientific paper

10.1016/0370-2693(94)01374-L

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 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 $2d$ gravity field that turns out to be on the genus-$n>1$ Riemann surfaces.

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