General Abelian Orientifold Models and One Loop Amplitudes

TL;DR

This work develops a general formalism for computing one-loop open-string amplitudes in Abelian orientifold models across arbitrary complex dimensions, providing explicit Klein bottle, Möbius strip, and cylinder expressions with a projective action of the orientifold group on Chan-Paton factors. It shows that tadpole cancellation imposes stringent, often universal, constraints on D-brane content and the action of the point group, revealing that orientifold planes strongly govern D-brane dynamics and typically fix the total number of D-branes to $32$. The analysis explains Zwart’s inconsistencies in certain $Z_4$-related cross-models via lattice and representation arguments, and outlines a path to generalize the approach to more complex point groups and discrete torsion. The results illuminate how orientifold planes shape gauge-group structure and brane configurations in higher-dimensional compactifications, with implications for model-building in string theory. $32$

Abstract

We construct a one loop amplitude for any Abelian orientifold point group for arbitary complex dimensions. From this we show several results for orientifolds in this general class of models as well as for low dimensional compactifications. We also discuss the importance and structure of the contribution of orientifold planes to the dynamics of D-branes, and give a physical explaination for the inconsistency of certain Z_4 models as discovered by Zwart.