Exoflops in Two Dimensions

TL;DR

This paper investigates exoflops in two-dimensional K3 surfaces, analyzing their geometric and categorical properties, and relating them to noncommutative resolutions, with implications for D-brane physics.

Contribution

It characterizes exoflops in K3 surfaces, distinguishes their dependence on rational curve types, and explores their categorical and physical implications.

Findings

Exoflops occur when rational curves in K3 surfaces shrink and reemerge outside the original manifold.

The nature of the curve (line or conic) determines whether the contraction leads to an orbifold or exoflop.

The D-brane category and massless D-branes are explicitly described in the exoflop limit.

Abstract

An exoflop occurs in the gauged linear $\sigma$-model by varying the Kahler form so that a subspace appears to shrink to a point and then reemerge "outside" the original manifold. This occurs for K3 surfaces where a rational curve is "flopped" from inside to outside the K3 surface. We see that whether a rational curve contracts to an orbifold phase or an exoflop depends on whether this curve is a line or conic. We study how the D-brane category of the smooth K3 surface is described by the exoflop and, in particular, find the location of a massless D-brane in the exoflop limit. We relate exoflops to noncommutative resolutions.