## D3-branes on partial resolutions of abelian quotient singularities of Calabi-Yau threefolds

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.

### Duke Scholars

## Published In

## DOI

## ISSN

## Publication Date

## Volume

## Issue

## Start / End Page

## Related Subject Headings

- Nuclear & Particles Physics
- 5107 Particle and high energy physics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
- 0105 Mathematical Physics

### Citation

*Nuclear Physics B*,

*566*(3), 599–641. https://doi.org/10.1016/S0550-3213(99)00646-X

*Nuclear Physics B*566, no. 3 (February 7, 2000): 599–641. https://doi.org/10.1016/S0550-3213(99)00646-X.

*Nuclear Physics B*, vol. 566, no. 3, Feb. 2000, pp. 599–641.

*Scopus*, doi:10.1016/S0550-3213(99)00646-X.

## Published In

## DOI

## ISSN

## Publication Date

## Volume

## Issue

## Start / End Page

## Related Subject Headings

- Nuclear & Particles Physics
- 5107 Particle and high energy physics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
- 0105 Mathematical Physics