Exoflops in two dimensions
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.
KeywordsD-branes Superstring Vacua Conformal Field Models in String Theory
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- R. Rouquier, Categorification of sl2 and braid groups, in Trends in representation theory of algebras and related topics, Contemp. Math. 406 (2006) 137, American Mathematical Society, Providence U.S.A. (2006).Google Scholar
- R. Anno, Spherical functors, arXiv:0711.4409.
- N. Addington, New derived symmetries of some hyperkähler varieties, arXiv:1112.0487.
- D. Orlov, Derived categories of coherent sheaves and triangulated categories of singularities, in Algebra, arithmetic, and geometry: in honor of Yu.I. Manin, vol. II, Progr. Math. 270 (2009) 503, Birkhäuser, Boston U.S.A. (2009) [math.AG/0503632].
- L.L. Avramov and D.R. Grayson, Resulutions and cohomology over complete intersections, in D. Eisenbud et al. eds., Computations in algebraic geometry with Macaulay 2, Algorithms and Computations in Mathematics 8, pp. 131-178, Springer-Verlag (2001).Google Scholar
- D. Halpern-Leistner and I. Shipman, Autoequivalences of derived categories via geometric invariant theory, arXiv:1303.5531.
- M. Van den Bergh, Non-commutative crepant resolutions, in The legacy of Niels Henrik Abel: the Abel bicentennial, Oslo 2002, Springer (2004), pp. 749-770 [math.RA/0211064].