Type IIB orientifolds, D‐brane instantons and the LARGE volume scenario

Abstract

This review article is concerned with three topics important for the construction of four‐dimensional models of particle physics in the context of type II String Theories. Special emphasis is put on a consistent presentation of these topics as well as on highlighting their interconnections. The first of the three topics deals with the tadpole cancellation conditions and the cancellation of chiral anomalies for type IIB orientifolds with orientifold three‐ and seven‐planes. The second topic is related to non‐perturbative effects originating from D‐brane instantons. In particular, in the presence of a realistic particle physics sector, a chiral zero‐mode constraint for contribution of instantons to the superpotential arises. The third topic is about moduli stabilisation in type IIB string compactifications. Two scenarios, the KKLT and Large Volume Scenario, are reviewed and a model for the latter scenario with the chiral zero‐mode constraint taken into account is presented.

A flux-scaling scenario for high-scale moduli stabilization in string theory

“…As usual, such a term implies a gauging of shift symmetries of the zero-forms dual to C 2,a in four dimensions. In the present setting, we have the relation (see for instance [78])…”

“…Compactifications of type IIB string theory on Calabi-Yau orientifolds with O7and O3-planes are well-studied. Here, we recall only some results which are needed below; for more details we would like to refer the reader to the original papers [75][76][77], and for a broader overview for instance to [4,78].…”

“…A stack of N such brane-image-brane pairs contributes to the D7-, D5-and D3brane tadpole equations (2.32). For the present setting, we can refer for instance to [83,85] (see also [78] for a more extended discussion) for the contribution to the tadpoles. With χ(Σ) the Euler number of the four-cycle Σ wrapped by the D7-brane, we find…”

Moduli Stabilization with Non‐Geometric Fluxes — Comments on Tadpole Contributions and de‐Sitter Vacua

“…We consider type IIB string theory on subject to an orientifold projection of the form . F L denotes the left‐moving fermion number and Ω P is the world‐sheet parity operator, and their action on the type IIB field content can be found for instance in [32]. The compact space is chosen to be a Calabi‐Yau three‐fold, and we impose a holomorphic involution σ on such that its Kähler and holomorphic three‐form satisfy and .…”

Non-geometric backgrounds in string theory

“…The corresponding world-volume actions contain Chern-Simons couplings to the R-R potentials C q which read (for reviews see e.g. [222,267])…”