  Motivated by the AdS/CFT correspondence, we show that there is a remarkable
agreement between static supergravity solutions and extrema of a field theory
potential. For essentially any function V, there are boundary conditions in
anti de Sitter space so that gravitational solitons exist precisely at the
extrema of V and have masses given by the value of V at these extrema. Based on
this, we propose new positive energy conjectures. On the field theory side,
each function V can be interpreted as the effective potential for a certain
operator in the dual field theory.
