Abstract
An exoflop occurs in the gauged linear σ-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.
Highlights
In the ambient toric variety will determine whether an orbifold phase or an exoflop phase occurs on their contraction
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
A typical hypersurface Calabi-Yau in a toric variety has a huge number of phases and many of these phases involve exoflops
Summary
Consider a smooth curve C of degree m in P2. The case m = 1 is a line and the case m = 2 is a conic. Let M denote the corresponding toric variety. This is viewed as a natural compactification of the “moduli space of complexified Kahler forms” and is of dimension r. Each regular triangulation of A corresponds to a phase and corresponds to a point in M. This point is called the “phase limit”. A one-dimensional edge of the secondary polytope corresponds to a toric rational curve in M “joining” two phase limits. This is associated to a perestroika (see section 7.2.C of [7]). This rational curve has three interesting points — the two phase limits and the intersection with ∆
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