Algebraic geometry and the geometry of quantum strings
Abstract
The p-loop amplitude of closed oriented bosonic strings in 26 dimensions is considered. The integration measure in this case is a measure on the moduli space M¯ p of Riemann surfaces of genus p. It is proved that for p > 1 this measure is a squared modulus of a holomorphic function having a second order pole on degenerate surfaces, divided by (det N1) 13. N1 is a matrix of scalar products of holomorphic one-forms on a surface. This property fixes the measure uniquely; this can be derived either by a direct calculation, or using a theorem of Mumford.
- Publication:
-
Physics Letters B
- Pub Date:
- March 1986
- DOI:
- 10.1016/0370-2693(86)90963-9
- Bibcode:
- 1986PhLB..168..201B