Categories of massless D-branes and del Pezzo surfaces

Self Cite

An exoflop occurs in the gauged linear σ-model by varying the Kähler 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.

Section: Introductionmentioning

confidence: 90%

Exoflops in two dimensions

Aspinwall

2015

Self Cite

“…There could be a large radius limit point in M A that is not a phase limit point. Such cases, associated to flops, were discussed in [19,20]. More general cases are presumably possible.…”

Section: Geometrymentioning

confidence: 99%

“…This picks out a certain class of triangulations of A . If the phase has a geometrical interpretation, it will typically be an "exoflop" phase [20]. This has a line or surface "sticking out" of a singular Calabi-Yau component.…”

Section: Extremal Transitions and Breaking The Reflexive Conditionmentioning

confidence: 99%

“…Locally, at the point X Σ , the geometry of V Σ is C 5 /Z 256 with group generator acting with weights 1 256 (1,251,20,176,64). We have therefore shown that the mirror of the quintic X Σ Figure 4: A Hidden Landau-Ginzburg Theory.…”

Section: A Reflexive Modelmentioning

confidence: 99%

“…To see the former use section 4 of[27]. To see the latter use the action of S A on K-theory as in section 5.1.6 of[20].…”

mentioning

confidence: 99%

See 2 more Smart Citations

General mirror pairs for gauged linear sigma models

Aspinwall

Plesser

2015

Self Cite

We carefully analyze the conditions for an abelian gauged linear σ-model to exhibit nontrivial IR behavior described by a nonsingular superconformal field theory determining a superstring vacuum. This is done without reference to a geometric phase, by associating singular behavior to a noncompact space of (semi-)classical vacua. We find that models determined by reflexive combinatorial data are nonsingular for generic values of their parameters. This condition has the pleasant feature that the mirror of a nonsingular gauged linear σ-model is another such model, but it is clearly too strong and we provide an example of a non-reflexive mirror pair. We discuss a weaker condition inspired by considering extremal transitions, which is also mirror symmetric and which we conjecture to be sufficient. We apply these ideas to extremal transitions and to understanding the way in which both Berglund-Hübsch mirror symmetry and the Vafa-Witten mirror orbifold with discrete torsion can be seen as special cases of the general combinatorial duality of gauged linear σ-models. In the former case we encounter an example showing that our weaker condition is still not necessary.

Hybrid conformal field theories

Bertolini

Melnikov

Plesser

2014

We describe a class of (2,2) superconformal field theories obtained by fibering a Landau-Ginzburg orbifold CFT over a compact Kähler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model, our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of linear models and comparing spectra among the phases.