Axion Inflation in Type II String Theory

TL;DR

This work investigates the viability of axion-driven inflation with many fields (N-flation) within Type IIB string theory, focusing on axions from RR two-forms on vanishing cycles and the role of world-sheet and D-brane corrections. It shows that large axion decay constants near Planck scale can arise near vanishing cycles (e.g., the resolved conifold), while large-volume limits suppress them; nonperturbative effects from D1 instantons and gaugino condensates on D5 branes generate the necessary axion potentials. A concrete $ obreak
$ orientifold setup and a toy model with N conifolds demonstrate that a mass hierarchy between axions and non-axionic partners can be achieved and that an inflationary regime with potentially observable tensor modes is possible in principle. The results highlight promising geometric regimes where axion N-flation could be realized, though they rely on delicate control of corrections and specific compactifications that remain to be explicitly constructed.

Abstract

Inflationary models driven by a large number of axion fields are discussed in the context of type IIB compactifications with N=1 supersymmetry. The inflatons arise as the scalar modes of the R-R two-forms evaluated on vanishing two-cycles in the compact geometry. The vanishing cycles are resolved by small two-volumes or NS-NS B-fields which sit together with the inflatons in the same supermultiplets. String world-sheets wrapping the vanishing cycles correct the metric of the R-R inflatons. They can help to generate kinetic terms close to the Planck scale and a mass hierarchy between the axions and their non-axionic partners during inflation. At small string coupling, D-brane corrections are subleading in the metric of the R-R inflatons. However, an axion potential can be generated by D1 instantons or gaugino condensates on D5 branes. Models with sufficiently large number of axions admit regions of chaotic inflation which can stretch over the whole axion field range for potentials from gaugino condensates. These models could allow for a possibly detectable amount of gravitational waves with tensor to scalar ratio as high as r<0.14.

Figures (5)

• Figure 1: Potential for one axion field $\theta$ with $\mu=1$.
• Figure 2: Potential for one axion field $\theta$ with $M>3$.
• Figure 3: Axion valley potential $V_{\rm eff}(G)$ (multiplied by $10^{11}$) for axion $\text{Re}\, G$ and its non-axionic partner $\text{Im}\, G$, at fixed $\langle T_{\rm R}\rangle$ and $\langle T_{i} \rangle$.
• Figure 4: Axion valley potential $V_{\rm eff}(G)$ in the absence of a superpotential depending on $G$. The axion direction $\text{Re}\, G$ is flat, while $\text{Im}\, G$ still has a minimum.
• Figure 5: Potential as function of conifold volume $v$ and B-field $b$. $R,c$ are fixed to minimum.