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

A.J. Amsel T. Hertog 1 S. Hollands D. Marolf
APC (UMR_7164) - AstroParticule et Cosmologie, Institut für theoretische Physik
Abstract : 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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Submitted on : Wednesday, March 21, 2007 - 4:04:52 PM
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A.J. Amsel, T. Hertog, S. Hollands, D. Marolf. A tale of two superpotentials: Stability and Instability in Designer Gravity. Physical Review D, American Physical Society, 2007, 75, pp.084008. ⟨10.1103/PhysRevD.75.084008⟩. ⟨in2p3-00137678⟩



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