BPS Chaos and Fortuity in Higgs Branches I: The Gepner Point

Abstract

The BPS states in Calabi-Yau compactifications of type II string theory can sometimes be described using quiver quantum mechanics whose Higgs branch is a complete intersection manifold. Their degeneracy resembles that of BPS black holes. A small fraction of these states corresponds to multi-center supergravity brane configurations and can be continued to the (near-Higgs) Coulomb branch. We identify them as monotone states. The overwhelming majority of states, known as pure-Higgs states, are fortuitous states, which concentrate at a particular $R$-charge. This division has a precise mathematical meaning as two different types of cohomologies of the Higgs branch target space. We argue that a natural probe of BPS chaos in these models is the Berry/Chern curvature. In the case of the Gepner model, we use localization techniques in an auxiliary two-dimensional CFT to compute the curvature, its RMT properties, and deviations from it.