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We construct new solutions of ten-dimensional supergravity with sixteen supercharges which describe the backreaction of Dp-branes with spherical worldvolume. These solutions are holographically dual to the (p+1)-dimensional maximally supersymmetric Yang-Mills theory on S^p+1. The finite size of the sphere provides an IR cut-off for the gauge theory which is manifested in the supergravity solution as a smooth cap-off of the geometry. In the UV the size of the sphere plays no role and thedoi:10.1007/jhep08(2018)029 fatcat:nya3njq3z5fadhrb3uqtzjihae