Large Field Inflation from Axion Mixing

TL;DR

This work shows that large-field inflation can be achieved with sub-Planckian axion decay constants by exploiting kinetic mixing in a non-diagonal axion moduli-space metric and Stückelberg couplings to a $U(1)$ gauge field, circumventing the need for decay-constant alignment or monodromy. By diagonalizing the axion sector and integrating out heavy fields, a single light axion with a cosine potential emerges, enabling natural inflation in a minimal 2-axion setup; string theory embeddings in Type II frameworks (Type IIA with D6-branes and Type IIB with D7-branes) illustrate how these mixings arise and can be realized in concrete geometries, such as toroidal orientifolds and Swiss-Cheese Calabi-Yau orientifolds. The analysis highlights the roles of anomaly cancellation (Green-Schwarz mechanism, possible generalized CS terms) and moduli stabilization as key challenges, while offering explicit isotropy conditions and parametric regions where trans-Planckian effective decay constants may be achieved. Overall, the approach provides a robust, string-friendly pathway to minimal, controllable large-field inflation via axion mixing with broad implications for model building and phenomenology.

Abstract

We study the general multi-axion systems, focusing on the possibility of large field inflation driven by axions. We find that through axion mixing from a non-diagonal metric on the moduli space and/or from Stückelberg coupling to a U(1) gauge field, an effectively super-Planckian decay constant can be generated without the need of "alignment" in the axion decay constants. We also investigate the consistency conditions related to the gauge symmetries in the multi-axion systems, such as vanishing gauge anomalies and the potential presence of generalized Chern-Simons terms. Our scenario applies generally to field theory models whose axion periodicities are intrinsically sub-Planckian, but it is most naturally realized in string theory. The types of axion mixings invoked in our scenario appear quite commonly in D-brane models, and we present its implementation in type II superstring theory. Explicit stringy models exhibiting all the characteristics of our ideas are constructed within the frameworks of Type IIA intersecting D6-brane models on T6/OR and Type IIB intersecting D7-brane models on Swiss-Cheese Calabi-Yau orientifolds.

Figures (5)

• Figure 1: Each quadrant of the unit circle corresponds to a region in the parameter space $(\theta,\Sigma)$, depending on the sign of metric entry ${\cal G}_{12}$ and the relative magnitude between ${\cal G}_{11}$ and ${\cal G}_{22}$, namely $\Sigma^2 \leq 1$ or $\Sigma^2 \geq 1$.
• Figure 2: Contour plot for example 1 with discrete parameters $2 k^1 = k^2 = 2 r_1 = 2 r_2$, and with $0<\Sigma\leq 1$ (left) or $\Sigma\geq1$ (right). Black regions correspond to unphysical values for $f_{\tilde{\xi}}$, while the physical values follow the color-coding from small (green) to large (red).
• Figure 3: Contour plot for example 2 with discrete parameters $k^1 = 2 k^2 = r_1 = 2 r_2$, and with $0<\Sigma\leq 1$ (left) or $\Sigma\geq1$ (right). Black regions correspond to unphysical values for $f_{\tilde{\xi}}$, while the physical values follow the color-coding from small (green) to large (red).
• Figure 4: Contour plot for example 3 with discrete parameters $k^1 = -2 k^2 = r_1 = 2 r_2$, and with $0<\Sigma\leq 1$ (left) or $\Sigma\geq1$ (right). Black regions correspond to unphysical values for $f_{\tilde{\xi}}$, while the physical values follow the color-coding from small (green) to large (red).
• Figure 5: (left) a-type lattice for a rectangular two-torus $T_{(i)}^2$ with area $R_1^{(i)} R_2^{(i)}$ and modular parameter $\tau^{(i)} = i\, R_2^{(i)}/ R_1^{(i)}$, and (right) b-type lattice for a tilted two-torus $T_{(i)}^2$ with area $R_1^{(i)} R_2^{(i)} \sin \theta_i$ and modular parameter $\tau^{(i)} = R_2^{(i)}/ R_1^{(i)} e^{i\, \theta_i}$. On a rectangular lattice the fixed planes under the $\Omega\mathcal{R}$-projection are located at $\text{Im}\,(z^i) = 0$ and $\text{Im}\,(z^i) = 1/2$, while a tilted torus-lattice only has one fixed plane under the $\Omega\mathcal{R}$-projection, namely $\text{Im}\,(z^i) = 0$. The basic one-cycles $\pi_{2i-1}$ and $\pi_{2i}$ transform as follows under the $\Omega\mathcal{R}$-projection: $\pi_{2i-1} \stackrel{\Omega\mathcal{R}}{\longrightarrow} \pi_{2i-1} - 2b^i \pi_{2i}$ and $\pi_{2i} \stackrel{\Omega\mathcal{R}}{\longrightarrow} - \pi_{2i}$, where the discrete parameter $b^i$ captures whether the two-torus $T^{2}_{(i)}$ is rectangular $(b^i = 0)$ or tilted $(b^i=1/2)$.