Volume Stabilization and the Origin of the Inflaton Shift Symmetry in String Theory

TL;DR

Problem: Realizing flat inflaton potentials in string theory while stabilizing the compactification volume. Approach: derive the inflaton shift symmetry from the intrinsic special-geometry and coset structure in type IIB on $K3\times T^2/\mathbb{Z}_2$ with D3/D7 moduli, via the ADFT construction and no-prepotential frame. Contributions: show that in both D7- and D3-moduli sectors the shift symmetry is an exact consequence of the $SO(2,2+n)$ coset and the period matrix, and that volume-stabilizing nonperturbative effects respect this symmetry, yielding a potential with $W = W_0 + A e^{-a\rho}$. Significance: provides a microscopic, symmetry-based mechanism for flat inflaton potentials in string cosmology, linking special geometry, dualities, and cosmological model-building.

Abstract

The main problem of inflation in string theory is finding the models with a flat potential, consistent with stabilization of the volume of the compactified space. This can be achieved in the 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 K3xT^2/Z 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)]x[SO(2,2+n)/(SO(2)x 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.