The AdS/CFT Correspondence and a New Positive Energy Conjecture for General Relativity

TL;DR

This paper explores the AdS/CFT correspondence with supersymmetry-breaking boundary conditions, proposing a new positive energy conjecture for asymptotically locally Anti-de Sitter spacetimes based on stability analysis.

Contribution

It introduces a novel positive energy conjecture for certain spacetimes, supported by stability analysis of the candidate minimum energy solution.

Findings

Supergravity solutions have negative energy consistent with Casimir energy.

The proposed minimum energy solution is stable against quadratic metric fluctuations.

A new positive energy theorem for asymptotically locally AdS spacetimes is suggested.

Abstract

We examine the AdS/CFT correspondence when the gauge theory is considered on a compactified space with supersymmetry breaking boundary conditions. We find that the corresponding supergravity solution has a negative energy, in agreement with the expected negative Casimir energy in the field theory. Stability of the gauge theory would imply that this supergravity solution has minimum energy among all solutions with the same boundary conditions. Hence we are lead to conjecture a new positive energy theorem for asymptotically locally Anti-de Sitter spacetimes. We show that the candidate minimum energy solution is stable against all quadratic fluctuations of the metric.