Towards Matter Inflation in Heterotic String Theory

Recently, a class of inflation models in supergravity with gauge non-singlet matter fields as the inflation has been proposed. It is based on a 'tribrid' structure in the superpotential and on a 'Heisenberg symmetry' for solving the η-problem. We suggest that a generalization of this model class may be suitable for realising inflation in heterotic orbifold compactifications, where the Heisenberg symmetry is a property of the tree-level Kähler potential of untwisted matter fields. We discuss moduli stabilization in this setup and propose a mechanism to stabilize the modulus associated to the inflation, which respects the symmetry in the large radius limit. Inflation ends via a `waterfall' phase transition, as in hybrid inflation. We give conditions which have to be satisfied for realising inflation along these lines in the matter sector of heterotic orbifolds.