Constraints and Period Relations in Bosonic Strings at Genus-g

TL;DR

This paper explores how boundary conditions in closed bosonic strings influence period relations among basis 1-forms at the quantum level, comparing Hamiltonian formalism results with classical Riemann relations.

Contribution

It demonstrates the derivation of period relations from quantum constraints using the KN formalism, linking boundary conditions to geometric properties of string world-sheets.

Findings

Quantum constraints induce relations among periods of basis 1-forms.

Comparison shows differences between quantum and classical Riemann period relations.

Highlights the role of boundary conditions in string theory geometry.

Abstract

We examine some of the implications of implementing the usual boundary conditions on the closed bosonic string in the hamiltonian framework. Using the KN formalism, it is shown that at the quantum level, the resulting constraints lead to relations among the periods of the basis 1-forms. These are compared with those of Riemanns' which arise from a different consideration.