The Bosonic String Measure at Two and Three Loops and Symplectic Transformations of the Volume Form

Abstract

Symplectic modular invariance of the bosonic string partition function has been verified at genus 2 and 3 using the period matrix coordinatization of moduli space. A calculation of the transformation of the holomorphic part of the differential volume element shows that an extra phase arises together with the factor associated with a specific modular weight; the phase is cancelled in the transformation of the entire volume element including the complex conjugate. An argument is given for modular invariance of the reggeon measure at genus twelve.

9 pages, DAMTP-R/94/29

References in corpus (2)

• Finiteness and Unitarity of Lorentz-Covariant Green-Schwarz Superstring Amplitudes
• Divergences in the Moduli Space Integral and Accumulating Handles in the Infinite-Genus Limit

Cited by in corpus (1)

• Linear relations among holomorphic quadratic differentials and induced Siegel's metric on M_g