Abstract:
We investigate field theories on the world-volume of a D3-brane transverse to partial resolutions of a ℤ3 × ℤ3 Calabi-Yau threefold quotient singularity. We deduce the field content and Lagrangian of such theories and present a systematic method for mapping the moment map levels characterizing the partial resolutions of the singularity to the Fayet-Iliopoulos parameters of the D-brane world-volume theory. As opposed to the simpler cases studied before, we find a complex web of partial resolutions and associated field-theoretic Fayet-Iliopoulos deformations. The analysis is performed by toric methods, leading to a structure which can be efficiently described in the language of convex geometry. For the world-volume theory, the analysis of the moduli space has an elegant description in terms of quivers. As a by-product, we present a systematic way of extracting the birational geometry of the classical moduli spaces, thus generalizing previous work on resolution of singularities by D-branes. © 2000 Elsevier Science B.V. All rights reserved.
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