Connecting flux vacua through scalar field excursions

TL;DR

This paper demonstrates how different flux vacua can be unified within a single scalar potential framework, enabling the computation of distances between vacua and supporting the Distance Conjecture through explicit string theory examples.

Contribution

It introduces an enlarged scalar field space that connects flux vacua, verifies the Distance Conjecture in this context, and relates unstable branes to the structure of the field space.

Findings

Distance between vacua can be computed using the field space metric.

Explicit examples confirm the Distance Conjecture in flux vacua.

Unstable branes are linked to the structure of the enlarged field space.

Abstract

We show how flux vacua that differ from each other in flux quanta can be seen as different vacua in a single scalar potential of an enlarged field space, which resolves the separation by thin domain walls. This observation, which is motivated by the AdS Distance Conjecture, allows one to compute distances between different vacua using the usual field space metric. We verify for explicit examples such as scale-seperated IIA flux vacua and the IIB Freund-Rubin vacua that the Distance Conjecture (for scalar fields) is satisfied and that the asymptotic directions in the enlarged field space are indeed hyperbolic. This enlarged field space contains the tachyon fields on the unstable $\tilde{\mathrm{D}}p$-branes of type II string theory, which can induce the brane charges of the stable D-branes. We suggest that requiring continuous interpolations refines the Cobordism Conjecture and postdicts the existence of unstable $\tilde{\mathrm{D}}p$-branes.