Minkowski 3-forms, Flux String Vacua, Axion Stability and Naturalness

TL;DR

This paper explores how Minkowski 3-forms influence flux string vacua, revealing their role in moduli stabilization, axion potential structure, and implications for inflation models and scalar mass stability.

Contribution

It demonstrates the connection between Minkowski 3-forms and flux vacua, showing their impact on axion potentials and perturbative corrections, with potential applications to inflation and scalar stability.

Findings

Minkowski 4-forms correspond to internal fluxes in string vacua.

Axion dependence in the scalar potential is mediated by these 4-forms.

Perturbative corrections to the potential likely expand in powers of the leading potential.

Abstract

We discuss the role of Minkowski 3-forms in flux string vacua. In these vacua all internal closed string fluxes are in one to one correspondence with quantized Minkowski 4-forms. By performing a dimensional reduction of the $D=10$ Type II supergravity actions we find that the 4-forms act as auxiliary fields of the Kahler and complex structure moduli in the effective action. We show that all the RR and NS axion dependence of the flux scalar potential appears through the said 4-forms. Gauge invariance of these forms then severely restricts the structure of the axion scalar potentials. Combined with duality symmetries it suggests that all perturbative corrections to the leading axion scalar potential $V_0$ should appear as an expansion in powers of $V_0$ itself. These facts could have an important effect e.g. on the inflaton models based on F-term axion monodromy. We also suggest that the involved multi-branched structure of string vacua provides for a new way to maintain interacting scalar masses stable against perturbative corrections.