Stable Non-BPS States in F- theory

TL;DR

The paper analyzes stable non-BPS states in F-theory on K3 by modeling them as string junctions between 7-branes and establishing stability through charge conservation combined with the isolation of a brane subset in moduli space. It develops a systematic framework to classify isolatable 7-brane configurations, distinguishing properly isolated and asymptotically isolated sets, and shows that only elliptic or parabolic monodromies can be isolated. Through explicit constructions, it identifies three realizations with stable non-BPS junctions: D1 near an O7 plane, an exotic affine E1, and affine E2 near a pair of O7 planes, and provides explicit data for all isolatable configurations including affine-type non-collapsible ones. The work also analyzes non-isolable configurations to illustrate limitations of the stability arguments and provides concrete examples of stable non-BPS states within isolated systems, thereby clarifying when genuinely new non-BPS sectors arise in F-theory on K3. Overall, it furnishes a constructive map from 7-brane configurations to potentially stable non-BPS spectra in this setup, with implications for non-perturbative dynamics in F-theory compactifications.

Abstract

F-theory on K3 admits non-BPS states that are represented as string junctions extending between 7-branes. We classify the non-BPS states which are guaranteed to be stable on account of charge conservation and the existence of a region of moduli space where the 7-branes supporting the junction can be isolated from the rest of the branes. We find three possibilities; the 7-brane configurations carrying: (i) the D_1 algebra representing a D7-brane near an orientifold O7-plane, whose stable non-BPS state was identified before, (ii) the exotic affine E_1 algebra, whose stable non-BPS state seems to be genuinely non-perturbative, and, (iii) the affine E_2 algebra representing a D7-brane near a pair of O7-planes. As a byproduct of our work we construct explicitly all 7-brane configurations that can be isolated in a K3. These include non-collapsible configurations of affine type.