Addington, N; Aspinwall, PS, *Categories of Massless D-Branes and del Pezzo Surfaces*,
J. High Energy Phys. 7(176):39pp., 2013, vol. 2013 no. 176
(May, 2013) [1305.5767v2], [doi] .
**Abstract:**

*In analogy with the physical concept of a massless D-brane, we define a
notion of "Q-masslessness" for objects in the derived category. This is defined
in terms of monodromy around singularities in the stringy Kahler moduli space
and is relatively easy to study using spherical functors. We consider several
examples in which del Pezzo surfaces and other rational surfaces in Calabi-Yau
threefolds are contracted. For precisely the del Pezzo surfaces that can be
written as hypersurfaces in weighted P3, the category of Q-massless objects is
a "fractional Calabi-Yau" category of graded matrix factorizations.*