Designer Gravity and Field Theory Effective Potentials

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