A tale of two superpotentials: Stability and Instability in Designer Gravity

Details A tale of two superpotentials: Stability and Instability in Designer Gravity A tale of two superpotentials: Stability and Instability in Designer Gravity

2007-01-05

arxiv.org/abs/hep-th/0701038v3

Phys.Rev.D75:084008,2007; Erratum-ibid.D77:049903,2008

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, 5 figures, RevTex; v2: references added; v3: corrected proof in Section V

Scientific paper

10.1103/PhysRevD.75.084008

We investigate the stability of asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass at or slightly above the Breitenlohner-Freedman bound. The boundary conditions in these ``designer gravity'' theories are defined in terms of an arbitrary function W. Previous work had suggested that the energy in designer gravity is bounded below if i) W has a global minimum and ii) the scalar potential admits a superpotential P. More recently, however, certain solutions were found (numerically) to violate the proposed energy bound. We resolve the discrepancy by observing that a given scalar potential can admit two possible branches of the corresponding superpotential, P_{\pm}. When there is a P_- branch, we rigorously prove a lower bound on the energy; the P_+ branch alone is not sufficient. Our numerical investigations i) confirm this picture, ii) confirm other critical aspects of the (complicated) proofs, and iii) suggest that the existence of P_- may in fact be necessary (as well as sufficient) for the energy of a designer gravity theory to be bounded below.

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