Field Theory Operator Encoding in Script N = 2 Geometries

We investigate supergravity solutions describing D5 branes wrapped on a twocycle which are dual to N=2 super Yang Mills theory. Brane probing thesesolutions allows the moduli space of the field theory to be identified. Thereare a unique set of coordinates in which the field theory on the probe takes anN=2 form and in these coordinates the running coupling of the gauge theory maybe identified. We show that the geometry, when restricted to the moduli space,takes a very simple form involving only two functions. One is the running gaugecoupling whilst the other parametrizes the scalar operators of the fieldtheory. The D5 brane distributions, for the full set of solutions in theliterature,can be determined by assuming the field theory's form for therunning coupling as a function of scalar vevs. We show that the resultingdistributions also correctly reproduce the scalar operators parametrizedelsewhere providing the first non-trivial consistency check on the duality.Comment: 11 page