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

TL;DR

The paper develops a clear 4-form language for flux string vacua, showing that all RR/NS axion dependence of the flux-induced potential is mediated by quantized Minkowski 4-forms that act as auxiliary fields for Kahler and complex-structure moduli. Through Dimensional reduction of Type II supergravity, the authors derive a positive-definite, no-scale–like scalar potential where the axion pieces enter exclusively via 4-forms, and they demonstrate that discrete shift symmetries plus dualities constrain perturbative corrections to be expansions in the leading potential $V_0$. The framework extends to open-string moduli (e.g., Higgs-otic inflation) and to geometric fluxes in IIA, as well as to IIB with GVW-type structures, revealing a universal 4-form–axion coupling pattern across corners of the string landscape. They further argue that the resulting multi-branched axions and 4-form gauge invariance can suppress dangerous radiative corrections, offering a natural mechanism for stabilizing interacting scalars and a potential route to large-field inflation that remains under perturbative control.

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.