Gauge-invariant formulation of the d=3 Yang-Mills theory

We write down the Yang-Mills partition function and the average Wilson loop in terms of local gauge-invariant variables bring the six components of th e metric tensor of dual space. The Wilson loop becomes the trace of the par allel transporter in curved space, else called the gravitational holonomy. We show that the external coordinates mapping the 3d curved space into a fl at 6d space play the role of glueball fields, and there is a natural mechan ism for the mass gap generation. (C) 2000 Elsevier Science B.V. All rights reserved.