Topological Ghosts: the Teeming of the Shrews

TL;DR

This paper explores the instability of spacetime-filling form fields with wrong sign kinetic terms in certain string theories, revealing how they can lead to increasing flux, potential vacuum decay, and implications for black hole formation and cosmology.

Contribution

It introduces a novel analysis of the dynamics of wrong sign kinetic form fields coupled to membranes, showing their instability and impact on vacuum energy and cosmological evolution.

Findings

Form fields with wrong sign kinetic terms are unstable when coupled to membranes.

The flux of these fields increases over time, contrary to typical decay scenarios.

This instability can lead to local negative vacuum energy and influence black hole formation.

Abstract

We consider dynamics of spacetime volume-filling form fields with "wrong sign" kinetic terms, such as in so-called Type-II$^*$ string theories. Locally, these form fields are just additive renormalizations of the cosmological constant. They have no fluctuating degrees of freedom. However, once the fields are coupled to membranes charged under them, their configurations are unstable: by a process analogous to Schwinger pair production the field space-filling flux increases. This reduces the cosmological constant, and preserves the null energy condition, since the processes that can violate it by reducing the form flux are very suppressed. The increase of the form flux implies that as time goes on the probability for further membrane nucleation {\it increases}, in contrast to the usual case where the field approaches its vacuum value and ceases to induce further transitions. Thus, in such models spaces with tiny positive vacuum energy are ultimately unstable, but the instability may be slow and localized. In a cosmological setting, this instability can enhance black hole rate formation, by locally making the vacuum energy negative at late times, which constrains the scales controlling membrane dynamics, and may even collapse a large region of the visible universe.