As a first step towards inflation in genuinely F-theoretic setups, we propose a scenario where the inflaton is the relative position of two 7-branes on holomorphic 4-cycles. Non-supersymmetric gauge flux induces an attractive inter-brane potential. The latter is sufficiently flat in the supergravity regime of large volume moduli. Thus, in contrast to brane-antibrane inflation, fluxbrane inflation does not require warping. We calculate the inflaton potential both in the supergravity approximation and via an open-string one-loop computation on toroidal backgrounds. This leads us to propose a generalisation to genuine Calabi-Yau manifolds. We also comment on competing F-term effects. The end of inflation is marked by the condensation of tachyonic recombination fields between the 7-branes, triggering the formation of a bound state described as a stable extension along the 7-brane divisor. Hence our model fits in the framework of hybrid D-term inflation. We work out the main phenomenological properties of our D-term inflaton potential. In particular, our scenario of D7/D7 inflation avoids the familiar observational constraints associated with cosmic strings.
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