Boundary Fixed Points, Enhanced Gauge Symmetry and Singular Bundles on K3

TL;DR

This paper explores fixed points in boundary conformal field theory related to D-branes on K3, revealing their role in geometric degenerations, enhanced gauge symmetries, and the structure of bound states and sheaves.

Contribution

It provides a detailed analysis of boundary fixed points in BCFT for D-branes on K3, linking them to geometric degenerations, gauge symmetry enhancement, and sheaf structures.

Findings

Fixed points correspond to degenerate brane configurations.

Enhanced gauge symmetries arise from projectively realized stabilizer groups.

Fixed points encode boundary of instanton moduli space and discrete torsion.

Abstract

We investigate certain fixed points in the boundary conformal field theory representation of type IIA D-branes on Gepner points of K3. They correspond geometrically to degenerate brane configurations, and physically lead to enhanced gauge symmetries on the world-volume. Non-abelian gauge groups arise if the stabilizer group of the fixed points is realized projectively, which is similar to D-branes on orbifolds with discrete torsion. Moreover, the fixed point boundary states can be resolved into several irreducible components. These correspond to bound states at threshold and can be viewed as (non-locally free) sub-sheaves of semi-stable sheaves. Thus, the BCFT fixed points appear to carry two-fold geometrical information: on the one hand they probe the boundary of the instanton moduli space on K3, on the other hand they probe discrete torsion in D-geometry.