The EZ-transformation massless D-brane conjecture

Let XX be a Calabi–Yau threefold containing a subspace EE, let i:EXi:E\hookrightarrow X be the inclusion, and let q:EZq:E\to Z be the map contracting EE to a lower-dimensional subspace ZZ. Write D(Z)\mathbf{D}(Z) for the bounded derived category of coherent sheaves on ZZ. EZ-transformation massless D-brane conjecture. Any D-brane that becomes massless at a point on a component of the discriminant associated with an EZ-transformation should be generated by objects of the form

iqz,zD(Z).i_*q^*\mathsf{z},\qquad \mathsf{z}\in\mathbf{D}(Z).

The conjecture proposes that the derived category of the contracted space ZZ describes the massless D-branes associated with the EZ-transformation; the source gives no resolution.

Sources & referencesView supporting material

Primary source

Paul S. Aspinwall, R. Paul Horja and Robert L. Karp, “Massless D-Branes on Calabi-Yau Threefolds and Monodromy”, arXiv:hep-th/0209161 (2002).

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