The paper explores the connection between field theories with sixteen supersymmetries and supergravity solutions, focusing on the large N limit. The authors consider D-branes in string theory and analyze the decoupling limit where the brane worldvolume theory decouples from gravity. They study the corresponding D-brane supergravity solutions and argue that these solutions can be trusted in certain regions where the curvature and effective string coupling are small. The supergravity solutions typically have multiple weakly coupled regions and interpolate between different limits of string-M-theory. The paper discusses various cases, including D2-branes, D1-branes, D0-branes, D4-branes, D5-branes, and D6-branes. For each case, the authors provide detailed analyses of the super-Yang-Mills theories and their dual supergravity descriptions. They explore the regions where perturbative super-Yang-Mills theory is valid and the regions where supergravity is applicable. The analysis reveals that the supergravity description is reliable in specific energy scales and regions, with transitions between different descriptions occurring at certain critical points. Key findings include: - For D2-branes, the super-Yang-Mills theory in 2+1 dimensions flows to a superconformal field theory with SO(8) R-symmetry in the UV and to a non-trivial background of type IIA supergravity in the IR. - For D1-branes, the theory flows to a free orbifold CFT in the IR and to a fundamental string solution in the UV. - For D0-branes, the theory is described by super quantum mechanics in the UV and by a gravitational wave background in eleven dimensions in the IR. - For D4-branes, the theory is described by a (0,2) six-dimensional conformal field theory on a circle in the UV and by type IIA supergravity in the IR. - For D5-branes, the theory is described by a classical solution of string theory in the UV and by NS fivebranes in the IR. - For D6-branes, the theory is not decoupled from the bulk, and there is no decoupled limit. The paper concludes with a discussion of near extremal configurations and the behavior of the theories at finite temperatures.The paper explores the connection between field theories with sixteen supersymmetries and supergravity solutions, focusing on the large N limit. The authors consider D-branes in string theory and analyze the decoupling limit where the brane worldvolume theory decouples from gravity. They study the corresponding D-brane supergravity solutions and argue that these solutions can be trusted in certain regions where the curvature and effective string coupling are small. The supergravity solutions typically have multiple weakly coupled regions and interpolate between different limits of string-M-theory. The paper discusses various cases, including D2-branes, D1-branes, D0-branes, D4-branes, D5-branes, and D6-branes. For each case, the authors provide detailed analyses of the super-Yang-Mills theories and their dual supergravity descriptions. They explore the regions where perturbative super-Yang-Mills theory is valid and the regions where supergravity is applicable. The analysis reveals that the supergravity description is reliable in specific energy scales and regions, with transitions between different descriptions occurring at certain critical points. Key findings include: - For D2-branes, the super-Yang-Mills theory in 2+1 dimensions flows to a superconformal field theory with SO(8) R-symmetry in the UV and to a non-trivial background of type IIA supergravity in the IR. - For D1-branes, the theory flows to a free orbifold CFT in the IR and to a fundamental string solution in the UV. - For D0-branes, the theory is described by super quantum mechanics in the UV and by a gravitational wave background in eleven dimensions in the IR. - For D4-branes, the theory is described by a (0,2) six-dimensional conformal field theory on a circle in the UV and by type IIA supergravity in the IR. - For D5-branes, the theory is described by a classical solution of string theory in the UV and by NS fivebranes in the IR. - For D6-branes, the theory is not decoupled from the bulk, and there is no decoupled limit. The paper concludes with a discussion of near extremal configurations and the behavior of the theories at finite temperatures.