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

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{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.

Authors:
;  [1];  [2];  [3]
  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)
Publication Date:
OSTI Identifier:
21020377
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.75.084008; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUNDARY CONDITIONS; COSMOLOGY; DE SITTER GROUP; GRAVITATION; INSTABILITY; MASS; MATHEMATICAL SOLUTIONS; POTENTIALS; SCALAR FIELDS; SCALARS; STABILITY; TACHYONS

Citation Formats

Amsel, Aaron J., Marolf, Donald, Hertog, Thomas, and Hollands, Stefan. A tale of two superpotentials: Stability and instability in designer gravity. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.084008.
Amsel, Aaron J., Marolf, Donald, Hertog, Thomas, & Hollands, Stefan. A tale of two superpotentials: Stability and instability in designer gravity. United States. doi:10.1103/PHYSREVD.75.084008.
Amsel, Aaron J., Marolf, Donald, Hertog, Thomas, and Hollands, Stefan. Sun . "A tale of two superpotentials: Stability and instability in designer gravity". United States. doi:10.1103/PHYSREVD.75.084008.
@article{osti_21020377,
title = {A tale of two superpotentials: Stability and instability in designer gravity},
author = {Amsel, Aaron J. and Marolf, Donald and Hertog, Thomas and Hollands, Stefan},
abstractNote = {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.},
doi = {10.1103/PHYSREVD.75.084008},
journal = {Physical Review. D, Particles Fields},
number = 8,
volume = 75,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}
  • No abstract prepared.
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  • Motivated by the anti-de Sitter conformal field theory correspondence, we show that there is remarkable agreement between static supergravity solutions and extrema of a field theory potential. For essentially any function V({alpha}) there are boundary conditions in anti--de Sitter space so that gravitational solitons exist precisely at the extrema of V and have masses given by the value of V at these extrema. Based on this, we propose new positive energy conjectures. On the field theory side, each function V can be interpreted as the effective potential for a certain operator in the dual field theory.
  • We consider asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass at or slightly above the Breitenlohner-Freedman bound in d{>=}4 spacetime dimensions. The boundary conditions in these ''designer gravity'' theories are defined in terms of an arbitrary function W. We give a general argument that the Hamiltonian generators of asymptotic symmetries for such systems will be finite, and proceed to construct these generators using the covariant phase space method. The direct calculation confirms that the generators are finite and shows that they take the form of the pure gravity result plus additional contributions from the scalar fields. Bymore » comparing the generators to the spinor charge, we derive a lower bound on the gravitational energy when W has a global minimum and the Breitenlohner-Freedman bound is not saturated.« less
  • Minor errors are corrected in several equations. The corrections do not change the conclusions, but for completeness the conclusions are restated more explicitly.