Deformations on Tilted Tori and Moduli Stabilisation at the Orbifold Point

TL;DR

This paper investigates how deformations of orbifold singularities on tilted tori influence moduli stabilization in Type IIA string models with D6-branes, showing certain moduli are stabilized at the orbifold point.

Contribution

It analyzes the effects of orbifold deformations on D6-branes in specific string compactifications, highlighting conditions for moduli stabilization and D-term generation.

Findings

D6-branes with U(N) gauge groups develop D-terms upon deformation.

Ten out of 15 twisted complex structure moduli are stabilized.

Deformations can be constrained or unconstrained depending on brane gauge groups.

Abstract

We discuss deformations of orbifold singularities on tilted tori in the context of Type IIA orientifold model building with D6-branes on special Lagrangian cycles. Starting from $T^6/(\mathbb{Z}_2 \times \mathbb{Z}_2)$, we mod out an additional $\mathbb{Z}_3$ symmetry to describe phenomenologically appealing backgrounds and reduce to $\mathbb{Z}_3$ and $\Omega\mathcal{R}$ invariant orbits of deformations. While D6-branes carrying SO(2N) or USp(2N) gauge groups do not constrain deformations, D6-branes with U(N) gauge groups develop non-vanishing D-terms if they couple to previously singular, now deformed cycles. We present examples for both types of D6-branes, and in a three-generation Pati-Salam model on $T^6/(\mathbb{Z}_2 \times \mathbb{Z}_6')$ we find that ten out of 15 twisted complex structure moduli are indeed stabilised at the orbifold point by the existence of the brane stacks.