Volume stabilization and the origin of the inflaton shift symmetry in string theory

One of the main problems of inflation in string theory is finding models with a flat potential while simultaneously stabilizing the volume of the compactified space. This can be achieved in theories where the potential has (an approximate) shift symmetry in the inflaton direction. We will identify a class of models where the shift symmetry uniquely follows from the underlying mathematical structure of the theory. It is related to the symmetry properties of the corresponding coset space and the period matrix of special geometry, which shows how the gauge coupling depends on the volume and the position of the branes. In particular, for type IIB string theory on K3 × T²/₂ with D3 or D7 moduli belonging to vector multiplets, the shift symmetry is a part of SO(2,2+n) symmetry of the coset space (SU(1,1)/U(1))×(SO(2,2+n)/(SO(2)×SO(2+n))). The absence of a prepotential, specific for the stringy version of supergravity, plays a prominent role in this construction, which may provide a viable mechanism for the accelerated expansion and inflation in the early universe.