Massless Spectra and Gauge Couplings at One-Loop on Non-Factorisable Toroidal Orientifolds

TL;DR

This paper explores how non-factorisable toroidal orientifolds can be analyzed using factorization techniques to compute massless spectra and gauge coupling corrections at one-loop, revealing effects on gauge group strength.

Contribution

It introduces a method to analyze non-factorisable orientifolds via factorization, enabling computation of gauge spectra and one-loop corrections using Conformal Field Theory.

Findings

Framework applied to $ ext{Z}_4 imes ext{O} ext{R}$ orientifolds on specific tori

One-loop corrections can strengthen gauge couplings

Demonstrated with a four-generation Pati-Salam model

Abstract

So-called `non-factorisable' toroidal orbifolds can be rewritten in a factorised form as a product of three two-tori by imposing an additional shift symmetry. This finding of Blaszczyk et al., arXiv:1111.5852, provides a new avenue to Conformal Field Theory methods, by which the vector-like massless matter spectrum - and thereby the type of gauge group enhancement on orientifold invariant fractional D6-branes - and the one-loop corrections to the gauge couplings in Type IIA orientifold theories can be computed in addition to the well-established chiral matter spectrum derived from topological intersection numbers among three-cycles. We demonstrate this framework for the $\mathbb{Z}_4 \times \Omega\mathcal{R}$ orientifolds on the $A_3 \times A_1 \times B_2$-type torus. As observed before for factorisable backgrounds, also here the one-loop correction can drive the gauge groups to stronger coupling as demonstrated by means of a four-generation Pati-Salam example.