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

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Amsel, Aaron J. ; Hertog, Thomas ; Hollands, Stefan ; Marolf, Donald (2007)

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.
  • References (41)
    41 references, page 1 of 5

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    [1] P. Breitenlohner and D. Z. Freedman, Ann. Phys. (N.Y.) 144, 249 (1982); Phys. Lett. B 115, 197 (1982).

    [2] M. Henneaux, C. Martinez, R. Troncoso, and J. Zanelli, Phys. Rev. D 65, 104007 (2002).

    [3] M. Henneaux, C. Martinez, R. Troncoso, and J. Zanelli, Phys. Rev. D 70, 044034 (2004).

    [4] T. Hertog and K. Maeda, J. High Energy Phys. 07 (2004) 051.

    [5] T. Hertog and G. T. Horowitz, Phys. Rev. Lett. 94, 221301 (2005).

    [6] T. Hertog and S. Hollands, Classical Quantum Gravity 22, 5323 (2005).

    [7] M. Henneaux, C. Martinez, R. Troncoso, and J. Zanelli, hep-th/0603185.

    [8] A. J. Amsel and D. Marolf, Phys. Rev. D 74, 064006 (2006).

    [9] S. Hollands and D. Marolf, gr-qc/0611044.

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