The effective action of type IIA Calabi–Yau orientifolds

Abstract

The N = 1 effective action for generic type IIA Calabi-Yau orientifolds in the presence of background fluxes is computed from a Kaluza-Klein reduction. The Kähler potential, the gauge kinetic functions and the flux-induced superpotential are determined in terms of geometrical data of the Calabi-Yau orientifold and the background fluxes. The moduli space is found to be a Kähler subspace of the N = 2 moduli space and shown to coincide with the moduli space arising in compactification of M-theory on a specific class of G 2 manifolds. The superpotential depends on all geometrical moduli and vanishes at leading order when background fluxes are turned off. The N = 1 chiral coordinates linearize the appropriate instanton actions such that instanton effects can lead to holomorphic corrections of the superpotential. Mirror symmetry between type IIA and type IIB orientifolds is shown to hold at the level of the effective action in the large volume -large complex structure limit.

Rigid D6-branes on $ {{{{T^6}}} \left/ {{\left( {{Z_2} \times {Z_{2M}} \times \Omega \mathcal{R}} \right)}} \right.} $ with discrete torsion

“…The massless closed string spectrum of IIA string theory on smooth Calabi-Yau-threefolds and its orientifold by ΩR has been discussed in detail in [94]. The multiplicities of multiplets in terms of Hodge numbers and the bosonic content of each multiplet are summarised in table 43, where the four dimensional bosonic degrees of freedom are obtained from the Four dimensionsal closed IIA spectra on Calabi-Yaus and their orientifolds N = 2 multiplet mult.…”

“…In the case with discrete torsion (η = −1), the exceptional contributions of the intersection numbers according to equation (97) have to be added, which can again be simplified using the twisted RR tadpole cancellation conditions (94) to (96) 2 invariant bulk three-cycles, we do not write out explicitly the K-theory constraints on T 6 /(Z 2 × Z 6 × ΩR) here.…”

Erratum to: “Towards the supersymmetric standard model from intersecting D6-branes on the Z6′ orientifold” [Nucl. Phys. B 755 (2006) 79]

“…In a supersymmetric orientifold RR tadpole cancellation ensures that NSNS tadpoles are also cancelled, but some moduli, (some of) of the complex structure moduli, the Kähler moduli and the dilaton, remain unstabilised. Recent developments have shown how such moduli may be stabilised using RR, NSNS and metric fluxes [22,23,24,25,26], and indeed Cámara, Font & Ibáñez [27,28] have shown how models similar to the ones we have been discussing can be uplifted into ones with stabilised Kähler moduli using a "rigid corset". In general, such fluxes contribute to tadpole cancellation conditions and might make them easier to satisfy.…”

On four-derivative terms in IIB Calabi-Yau orientifold reductions

“…In this section we perform the orientifold projection on the effective action (2.21), which amounts to adding O3/O7 planes to the Calabi-Yau background [1,5,6,8,[47][48][49][50]. For consistency we are required to also consider D3/D7 branes in this setup.…”