We consider field theories with sixteen supersymmetries, which includes U(N)
Yang-Mills theories in various dimensions, and argue that their large N limit
is related to certain supergravity solutions. We study this by considering a
system of D-branes in string theory and then taking a limit where the brane
worldvolume theory decouples from gravity. At the same time we study the
corresponding D-brane supergravity solution and argue that we can trust it in
certain regions where the curvature (and the effective string coupling, where
appropriate) are small. The supergravity solutions typically have several
weakly coupled regions and interpolate between different limits of
string-M-theory.Comment: 24 pages, latex. v2: reference added, v3: typos correcte
