A tale of two superpotentials: Stability and instability in designer gravity

Journal Article · Sun Apr 15 04:00:00 EDT 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.75.084008· OSTI ID:21020377

Amsel, Aaron J; Marolf, Donald ^[1]; Hertog, Thomas ^[2]; Hollands, Stefan ^[3]

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1. Physics Department, UCSB, Santa Barbara, California 93106 (United States)
2. Theory Division, CERN, CH-1211 Geneva 23 (Switzerland) and APC, 10 rue Alice Domon et Leonie Duquet, 75205 Paris (France)
3. Inst. f. Theor. Physik, Georg-August-Universitaet, D-37077, Goettingen (Germany)

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{sub {+-}}. When there is a P{sub -} branch, we rigorously prove a lower bound on the energy; the P{sub +} 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{sub -} may in fact be necessary (as well as sufficient) for the energy of a designer gravity theory to be bounded below.

• OSTI ID: 21020377
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 75; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
COSMOLOGY
DE SITTER GROUP
GRAVITATION
INSTABILITY
MASS
MATHEMATICAL SOLUTIONS
POTENTIALS
SCALAR FIELDS
SCALARS
STABILITY
TACHYONS