Designer Gravity and Field Theory Effective Potentials

TL;DR

This paper explores the correspondence between supergravity solutions and field theory potentials in the context of AdS/CFT, revealing that gravitational solitons align with extrema of effective potentials and proposing related positive energy conjectures.

Contribution

It establishes a direct link between supergravity solutions and extrema of effective potentials in dual field theories, introducing new positive energy conjectures.

Findings

Supergravity solutions correspond to extrema of field theory potentials.

Masses of gravitational solitons match potential values at extrema.

Proposes new positive energy conjectures in AdS/CFT context.

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.