Systematics of type IIB moduli stabilisation with odd axions

Abstract

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 (B2, C2) in type IIB are largely unexplored despite their relevance for inflationary model building. This article provides novel insights into the general structure of 4D $$ \mathcal{N} $$ N = 1 F-term scalar potentials at higher orders in the α′ and gs 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 (α′)3 corrections to the Kähler potential. By studying a partially SL(2, ℤ)-completed form of the Kähler 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.

Stabilising all Kähler moduli in perturbative LVS

“…Similarly for the case of BBHL's α corrections [15] being included, we have the following simplified expressions for P i and Pi which matches with those claimed in [34,36,37],…”

“…Here the indices {i, α} are such that i ∈ h 2,1 − (CY /O) while α ∈ h 1,1 + (CY /O). Moreover, we assume that h 1,1 = h 1,1 + for simplicity, and hence there are no so-called odd-moduli G a which are present in our analysis, and we refer the interested readers to [34]. Using the Kähler potential pieces given in eqs.…”

“…In [34] it was observed that the form of P1 remains the same even after including the odd-moduli, despite a complicated mixing with new terms in the generalized version of P 1 in the corresponding K S,S component of the Kähler metric.…”

Divisor topologies of CICY 3-folds and their applications to phenomenology

“…This is due to the larger frequency of finding what is called as "non-trivially identical divisors" (NIDs) of the CY 3-folds [19] which are relevant for constructing their orientifolds. This latter fact will generically lead to the presence of odd-moduli in the 4d Effective Field Theory (EFT), something that has attracted lots of attention in recent years and can be further explored for application in axionic phenomenology [19][20][21][22][23][24][25][26][27][28][29], specially for driving inflation and dark matter models. Also, motivated by the proposal of performing moduli stabilization using the so-called ample divisors [30] we have presented a classification of the ample divisors for all the favorable pCICYs, which we find to be always a non-rigid divisor.…”

“…Thus, given the richness of the pCICY dataset for the NIDs, it would be good for pursuing type IIB model building with odd-moduli which has attracted a significant amount of interest in recent years [25,29]. Let us consider some explicit examples for demonstrating these findings.…”