ADS MEMBRANES WRAPPED ON SURFACES OF ARBITRARY GENUS

We present and analyze solutions of D = 11 supergravity describing the ''near-horizon'' (i.e., asymptotically AdS(4) x S-7) geometry of M2-b ranes wrapped on surfaces of arbitrary genus. We study the forces expe rienced by test M2-branes in such backgrounds, and find evidence that extremal branes on surfaces of genera higher than the torus are unstab le. Using the holographic connection between AdS spaces and superconfo rmal field theories in the large N limit, we discuss the phases of the associated 2+1 dimensional theories. Finally, we also study the exten sion of these solutions to other branes, in particular to D2-branes. ( C) 1998 Elsevier Science B.V. All rights reserved.