Designer Gravity and Field Theory Effective Potentials

TL;DR

It is shown that there is remarkable agreement between static supergravity solutions and extrema of a field theory potential for essentially any function V(alpha) there are boundary conditions in anti-de Sitter space so that gravitational solitons exist precisely at the extrems of V and have masses given by the value of V at these extremas.

Abstract

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.

Figures (3)

• Figure 1: The function $\beta_s$ obtained from the solitons.
• Figure 2: The effective potential ${\cal V} (\alpha)=W_0 -\frac{1}{2}\alpha$.
• Figure 3: The effective potential ${\cal V} = W_0 -\frac{1}{4}\alpha^2 + \frac{1}{40}\alpha^3$.