Systematics of type IIB moduli stabilisation with odd axions

Moduli stabilisation in superstring compactifications on Calabi-Yau orientifolds remains a key challenge in the search for realistic string vacua. In particular, odd moduli arising from the reduction of 2-forms (B-2, C-2) in type IIB are largely unexplored despite their relevance for inflationary model building. This article provides novel insights into the general structure of 4D N = 1 F-term scalar potentials at higher orders in the alpha' and g(s) expansion for arbitrary Hodge numbers. We systematically examine superpotential contributions with distinct moduli dependences which are induced by fluxes or non-perturbative effects. Initially, we prove the existence of a no-scale structure for odd moduli in the presence of (alpha')(3) corrections to the Kahler potential. By studying a partially SL(2, Z)-completed form of the Kahler potential, we derive the exact no-scale breaking effects at the closed string 1-loop and non-perturbative D-instanton level. These observations allow us to present rigorous expressions for the F-term scalar potential applicable to arbitrary numbers of moduli in type IIB Calabi-Yau orientifold compactifications. Finally, we compute the Hessian for odd moduli and discuss potential phenomenological implications.

Automated summary

This article investigates the problem of moduli stabilisation in superstring compactifications on Calabi-Yau orientifolds and provides novel insights into the F-term scalar potential. By considering superpotential contributions with different moduli dependences, we prove the existence of a no-scale structure for odd moduli and derive the exact expressions for the no-scale breaking effects. Finally, we calculate the Hessian for odd moduli and discuss potential phenomenological implications.