Moduli Stabilization in Type IIB Orientifolds (II)

TL;DR

This paper analyzes conditions for moduli stabilization in type IIB orientifolds, identifying which manifolds allow KKLT scenarios and proposing mechanisms for stabilizing specific moduli, with implications for various orbifold compactifications.

Contribution

It identifies conditions under which KKLT moduli stabilization is possible in type IIB orientifolds and proposes a new mechanism for stabilizing odd cohomology moduli.

Findings

Certain orientifolds with h_(2,1)=0 are incompatible with KKLT stabilization.

A mechanism for stabilizing odd cohomology H^(1,1)_- moduli is proposed.

All moduli can be stabilized in specific resolved orbifold examples using fluxes and racetrack superpotentials.

Abstract

We discuss general properties of moduli stablization in KKLT scenarios in type IIB orientifold compactifications. In particular, we find conditions for the Kaehler potential to allow a KKLT scenario for a manifold X_6 without complex structure moduli, i.e. h_(2,1)(X_6)=0. This way, a whole class of type IIB orientifolds with h_(2,1)(X_6)=0 is ruled out. This excludes in particular all Z_N- and Z_N x Z_M-orientifolds X_6 with h_(2,1)(X_6)=0 for a KKLT scenario. This concerns Z_3, Z_7, Z_3 x Z_3, Z_4 x Z_4, Z_6 x Z_6 and Z_2 x Z_6' -both at the orbifold point and away from it. Furthermore, we propose a mechanism to stabilize the Kaehler moduli accociated to the odd cohomology H^(1,1)_-(X_6). In the second part of this work we discuss the moduli stabilization of resolved type IIB Z_N- or Z_N x Z_M - orbifold/orientifold compactifications. As examples for the resolved Z_6 and Z_2 x Z_4 orbifolds we fix all moduli through a combination of fluxes and racetrack superpotential.