Stability of non-supersymmetric vacua from calibrations

TL;DR

This paper explores extending calibration-based stability arguments to non-supersymmetric vacua in string theory, analyzing various AdS solutions and their resistance to decay channels.

Contribution

It introduces a calibration-based approach to protect non-supersymmetric vacua from decay, including new solutions involving complex geometries.

Findings

Many non-supersymmetric vacua resist decay channels assessed.

Calibrations can ensure stability of existing D-branes in non-supersymmetric backgrounds.

New AdS solutions involving coset spaces and fibrations are analyzed.

Abstract

Supersymmetric vacua are protected from vacuum decay by energy positivity. No such argument is known for any non-supersymmetric vacua. In this paper, we try to extend to the latter a simpler argument based on calibrations, to at least protect them from decays mediated by D-brane bubbles, including their abelian bound states. We examine several classes of AdS$_4$ and AdS$_5$ solutions in type II string theory, including some new ones, involving coset spaces, sphere fibrations, K\"ahler--Einstein manifolds. Many of these vacua have resisted against all the decay channels we were able to assess. We also show how to use calibrations for the stability of D-branes already present in a non-supersymmetric solution.