WILSON LOOPS, CONFINEMENT, AND PHASE-TRANSITIONS IN LARGE-N GAUGE-THEORIES FROM SUPERGRAVITY

We use the recently proposed supergravity approach to large N gauge th eories to calculate ordinary and spatial Wilson loops of gauge theorie s in various dimensions. In this framework we observe an area law for spatial Wilson loops in four and five dimensional supersymmetric Yang- Mills at finite temperature. This can be interpreted as the area law o f ordinary Wilson loops in three and four dimensional non-supersymmetr ic gauge theories at zero temperature which indicates confinement in t hese theories. Furthermore, we show that super Yang Mills theories wit h 16 supersymmetries at finite temperature do not admit phase transiti ons between the weakly coupled super Yang Mills and supergravity regim es. This result is derived by analyzing the entropy and specific heat of those systems as well as by computing ordinary Wilson loops at fini te temperature. The calculation of the entropy was carried out in all different regimes and indicates that there is no first order phase tra nsition in these systems. For the same theories at zero temperature we also compute the dependence of the quark anti-quark potential on the separating distance.