Wilson Line Inflation

TL;DR

The paper develops a general string-theory inflation framework in which the inflaton is a Wilson line in magnetized compactifications, showing how T-duality maps these models to standard brane-inflation scenarios. It derives a Wilson-line–dependent vacuum energy and an interaction potential, enabling hybrid-like inflation where a tachyonic open-string mode triggers the exit, potentially leaving cosmic strings. Embedding into KKLT-type moduli stabilization reveals that the eta problem can be evaded in explicit examples, with precise parameter choices yielding small slow-roll parameters, a quasi-unit spectral index, and negligible tensor modes, while allowing remnant cosmic strings with Gμ ≲ 10^{-7}. The work also argues for a unifying picture where all toroidal open-string inflationary configurations arise from magnetized D9-branes with Wilson lines and shows prospects for heterotic extensions and more complex compactifications.

Abstract

We present a general set-up for inflation in string theory where the inflaton field corresponds to Wilson lines in compact space in the presence of magnetic fluxes. T-dualities and limits on the value of the magnetic fluxes relate this system to the standard D-brane inflation scenarios, such as brane-antibrane inflation, D3/D7 brane inflation and different configurations of branes at angles. This can then be seen as a generalised approach to inflation from open string modes. Inflation ends when the Wilson lines achieve a critical value and an open string mode becomes tachyonic. Then hybrid-like inflation, including its cosmic string remnants, is realized in string theory beyond the brane annihilation picture. Our formalism can be incorporated within flux-induced moduli stabilisation mechanisms in type IIB strings. Also, contrary to the standard D-brane separation, Wilson lines can be considered in heterotic string models. We provide explicit examples to illustrate similarities and differences of our mechanism to D-brane inflation. In particular we present an example in which the eta-problem present in brane inflation models is absent in our case. We have examples with both blue and red tilted spectral index and remnant cosmic string tension $Gμ\lesssim 10^{-7}$.