D3-brane(s) in AdS5 x S5 and N=4, 2, 1 SYM

Recently, Douglas and Taylor proposed to identify the Higgs vev of the Coulomb branch of the 4 dimensional N = 4 super Yang-Mills theory with the positions of D3-branes in the AdS(5) x S-5 String theory. We extend this identification to more general configurations that preserve less supersymmetry. We show that a single D3-brane in AdS(5) x S-5 String theory can break the space-time supersymmetry to 1/4 or even 1/8. Such configurations, interpreted as backgrounds of the SYM, also break the N = 4 superconformal symmetry of SYM to 1/4 or 1/8, giving N = 2 or N = 1. We discuss the implications of this correspondence. We also present other BPS D3-brane configurations that preserve 1/8 supersymmetry corresponding to N = 1 on the SYM side. (C) 1999 Elsevier Science B.V.