GEOMETRY OF N=1 DUALITIES IN 4 DIMENSIONS

We discuss how N = 1 dualities in four dimensions are geometrically re alized by wrapping D-branes about 3-cycles of Calabi-Yau threefolds. I n this setup the N = 1 dualities for SU, SO and USp gauge groups with fundamental fields gee mapped to statements about the monodromy and re lations among 3-cycles of Calabi-Yau threefolds. The connection betwee n the theory and its dual requires passing through configurations whic h are T-dual to the well-known phenomenon of decay of BPS states in N = 2 field theories in four dimensions. We compare our approach to rece nt works based on configurations of D-branes in the presence of NS 5-b ranes and give simple classical geometric derivations of various exoti c dynamics involving D-branes ending on NS branes. (C) 1997 Elsevier S cience B.V.