On the normalization of open-closed string amplitudes

TL;DR

This paper determines the signs and normalizations of open-closed string amplitudes using factorization constraints, addressing sign ambiguities due to non-orientable moduli spaces, and establishing a consistent normalization scheme.

Contribution

It introduces a method to fix signs and normalizations of mixed open-closed string amplitudes by using specific conventions and factorization constraints.

Findings

Normalized amplitudes depend on genus, boundaries, insertions, coupling, and D-brane tension.

Resolved sign ambiguities by fixing conventions for moduli space integration and operator ordering.

Provided a consistent framework for open-closed string amplitude normalization.

Abstract

We use the factorization constraints of open-closed string field theory to determine the signs and normalizations of general string amplitudes with both open and closed string external states. The normalization of all amplitudes is controlled by the genus, the number of boundaries, the number of open and closed string insertions, the string coupling and the D-brane tension. The challenge with signs arises because the relevant moduli spaces are not complex manifolds and have no obvious orientation. We deal with this by fixing a specific convention for the sign of the integration measure over the moduli space and adopting a consistent prescription for the ordering of operators and ghost insertions inside correlators.