Deformations on tilted tori and moduli stabilisation at the orbifold point

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 /(Z 2 × Z 2 ), we mod out an additional Z 3 symmetry to describe phenomenologically appealing backgrounds and reduce to Z 3 and ΩR 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 /(Z 2 × 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.

On classical de Sitter and Minkowski solutions with intersecting branes

“…[29][30][31] for attempts of model building in this direction), allowing for fluxes and curved manifolds. Such a setup would help stabilizing closed string moduli, on top of the effects described in [32], so it should be interesting for such constructions.…”

Deforming D‐brane models on orbifolds

“…Both contain in general flat directions for the dilaton and geometric moduli. Our computations demonstrate that a large number of these flat directions can be stabilised [1] without introducing closed string background fluxes [2], which implies that no severe backreaction on the geometry occurs. In addition, our method is appropriate for calculating the tree-level value of gauge couplings by using periods over (special) Lagrangian ((s)Lag) three-cycles, where previously identical couplings g −2 a ∝ Π a |Ω 3 | can be tuned via deformations to obtain phenomenologically acceptable values [1,3].…”

“…We will describe the orbifolds as T 6 /(Z 2 × Z 2 ) /Z M , where ideally Z M does not lead to additional exceptional three-cycles, but restricts the way how the Z 2 × Z 2 singularities can be deformed. In particular, we will discuss the phenomenologically appealing T 6 /(Z 2 × Z 6 × ΩR) orientifold on the SU(3) 3 lattice [1].…”

“…We then find three Z 3 -triplets of Z 2 fixed points preserved by σ R with now real deformation parameters ε At first, we consider SO(8) 4 and USp(8) 4 models, where the D6-branes only wrap orientifold-even cycles, see [1] for details on the discrete data (wrapping numbers, displacements and Wilson lines). There exists no central U (1) factor, and therefore neither D-terms in the low-energy effective action nor a potential for the deformation moduli.…”

From stringy particle physics to moduli stabilisation and cosmology

“…More Z 2 twisted moduli can, however, be stabilised due to their couplings to D-branes as noted in [16,17]. As can be verified explicitly by computing the integral …”