On Real Intrinsic Wall Crossings

TL;DR

This paper uses real geometric methods to analyze the stability of BPS configurations and moduli spaces, revealing how scalar curvature and Fayet parameters influence phase structures and vacuum correlations.

Contribution

It introduces a geometric approach to study moduli space stability, linking scalar curvature to phase transitions and stability walls in gauge and string theories.

Findings

Scalar curvature indicates global vacuum correlations.

Divergences in scalar curvature suggest phase transitions.

Stability walls can be analyzed through polynomial Fayet parameter dependencies.

Abstract

We study moduli space stabilization of a class of BPS configurations from the perspective of the real intrinsic Riemannian geometry. Our analysis exhibits a set of implications towards the stability of the D-term potentials, defined for a set of abelian scalar fields. In particular, we show that the nature of marginal and threshold walls of stabilities may be investigated by real geometric methods. Interestingly, we find that the leading order contributions may easily be accomplished by translations of the Fayet parameter. Specifically, we notice that the various possible linear, planar, hyper-planar and the entire moduli space stabilities may easily be reduced to certain polynomials in the Fayet parameter. For a set of finitely many real scalar fields, it may be further inferred that the intrinsic scalar curvature defines the global nature and range of vacuum correlations. Whereas, the underlying moduli space configuration corresponds to a non-interacting basis at the zeros of the scalar curvature, where the scalar fields become un-correlated. The divergences of the scalar curvature provide possible phase structures, viz., wall of stability, phase transition, if any, in the chosen moduli configuration. The present analysis opens up a new avenue towards the stabilizations of gauge and string moduli.