Algebraic geometry and the geometry of quantum strings
Abstract
The ploop amplitude of closed oriented bosonic strings in 26 dimensions is considered. The integration measure in this case is a measure on the moduli space M̄ _{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 N_{1}) ^{13}. N_{1} is a matrix of scalar products of holomorphic oneforms 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:
 10.1016/03702693(86)909639
 Bibcode:
 1986PhLB..168..201B