D7-Brane Moduli Space in Axion Monodromy and Fluxbrane Inflation

TL;DR

This work analyzes the quantum-corrected moduli space of D7-brane position moduli in Type IIB/F-theory, focusing on two inflationary scenarios that rely on a shift-symmetric Kahler potential to keep the inflaton light. It shows that for large complex structure this shift symmetry is preserved (up to exponentially small corrections) and demonstrates how flux choices can suppress inflaton dependence in the superpotential while loop effects respect an extended no-scale structure. The authors construct explicit toy models and map the field-theory inflationary parameters to string-theory data, then perform a detailed phenomenological analysis of fluxbrane inflation, including moduli stabilization, loop corrections, and observational constraints, finding regions of parameter space that can reproduce the correct spectral index and amplitude with a small tensor mode. They also discuss the open-string landscape and flux vacua statistics, arguing that a substantial set of vacua at large complex structure can exist, offering room for cosmological constant tuning and brane stabilization within LVS frameworks.

Abstract

We analyze the quantum-corrected moduli space of D7-brane position moduli with special emphasis on inflationary model building. D7-brane deformation moduli are key players in two recently proposed inflationary scenarios: The first, D7-brane chaotic inflation, is a variant of axion monodromy inflation which allows for an effective 4d supergravity description. The second, fluxbrane inflation, is a stringy version of D-term hybrid inflation. Both proposals rely on the fact that D7-brane coordinates enjoy a shift-symmetric Kahler potential at large complex structure of the Calabi-Yau threefold, making them naturally lighter than other fields. This shift symmetry is inherited from the mirror-dual Type IIA Wilson line on a D6-brane at large volume. The inflaton mass can be provided by a tree-level term in the flux superpotential. It induces a monodromy and, if tuned to a sufficiently small value, can give rise to a large-field model of inflation. Alternatively, by a sensible flux choice one can completely avoid a tree-level mass term, in which case the inflaton potential is induced via loop corrections. The positive vacuum energy can then be provided by a D-term, leading to a small-field model of hybrid natural inflation. In the present paper, we continue to develop a detailed understanding of the D7-brane moduli space focusing among others on shift-symmetry-preserving flux choices, flux-induced superpotential in Type IIB/F-theory language, and loop corrections. While the inflationary applications represent our main physics motivation, we expect that some of our findings will be useful for other phenomenological issues involving 7-branes in Type IIB/F-theory constructions.

Figures (10)

• Figure 1: Plot of the potential \ref{['cosPot']}. For illustrative purposes the relative size of the variation with respect to the constant is exaggerated.
• Figure 2: Plot of the combined potential $\delta V = \sum_{i}\tilde{\alpha}_i \sin( \varphi_i/f)$
• Figure 3: Visualization of the base of $K3$, i.e. $T^2/\mathds{Z}_2$, in the orientifold limit. Only two of the sixteen D7-branes are shown.
• Figure 4: The dashed line represents the one-cycle of the flux three-cycle $M^i \Sigma_i$ on $T^2/\mathds{Z}_2$ while the straight line represents the branch cut of the logarithm in (\ref{['log-cut']}) with a D7-brane at its end.
• Figure 5: Mirror symmetry in the SYZ-picture. A Calabi-Yau is described as a $T^3$-fibration over a three dimensional base $B_3$. Mirror symmetry is realized as a chain of three T-duality transformations along the torus fiber, mapping a cycle of length $R^s$ to a cycle of length $1/R^s$.