D-branes on non-abelian threefold quotient singularities

We investigate the classical moduli space of D-branes on a non-abelian Cala bi-Yau threefold singularity and find that it admits topology-changing tran sitions. We construct a general formalism of world-volume field theories in the language of quivers and give a procedure for computing the enlarged Ka hler cone of the moduli space. The topology changing transitions achieved b y varying the Fayet-Iliopoulos parameters correspond to changes of lineariz ation of a geometric invariant theory quotient and can be studied by method s of algebraic geometry. Quite surprisingly, the structure of the enlarged Kahler cone can be computed by toric methods, By using this approach, we gi ve a detailed discussion of two low-rank examples. (C) 1999 Elsevier Scienc e B.V. All rights reserved.