Violation of Energy Bounds in Designer Gravity

TL;DR

This paper investigates the stability bounds in designer gravity theories with tachyonic scalars and demonstrates that certain energy bounds previously thought to hold can be violated under specific conditions.

Contribution

The study reveals that energy bounds in designer gravity theories are not universally valid, identifying cases where these bounds do not apply.

Findings

Energy bounds can be violated in certain designer gravity models.

Not all superpotentials ensure the lower energy bounds hold.

The results challenge previous assumptions about stability criteria.

Abstract

We continue our study of the stability of designer gravity theories, where one considers anti-de Sitter gravity coupled to certain tachyonic scalars with boundary conditions defined by a smooth function W. It has recently been argued there is a lower bound on the conserved energy in terms of the global minimum of W, if the scalar potential arises from a superpotential P and the scalar reaches an extremum of P at infinity. We show, however, there are superpotentials for which these bounds do not hold.