  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.
