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Instabilities in Anti-de Sitter Space

Instabilities in Anti-de Sitter Space. Ong Yen Chin LeCosPA Research Group Meeting 12 May 2011. Breitenlohner- F reedman Bound. A negative mass for a bulk scalar field in AdS(d+1) does not necessarily lead to any instabilities, provided that it isn’t too negative.

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Instabilities in Anti-de Sitter Space

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  1. Instabilities in Anti-deSitter Space Ong Yen ChinLeCosPAResearch Group Meeting 12 May 2011

  2. Breitenlohner-Freedman Bound A negative mass for a bulk scalar field in AdS(d+1) does not necessarily lead to any instabilities, provided that it isn’t too negative. We will work with LAdS=1. 2/15

  3. Breitenlohner-Freedman Bound Idea of Proof: Choose AdS wave equation is unstable if 3/15

  4. Breitenlohner-Freedman Bound We consider negative energy AdS wave equation: It has the solution: If i.e. there exist (discrete) normalizable states satisfying the AdS wave equation. 4/15

  5. Perturbative Instability For pure AdS, the BF bound is equivalent to the statement that the Laplacian has continuous spectrum on For asymptotically AdS space or quotients of AdS, there can exist discrete eigenvalues: Fields which saturate BF bound (and thus stable )in pure AdS can be unstable in asymptotically AdS space. 5/15

  6. 6/15

  7. Perturbative Instability For Einstein manifolds these modes can exist only when the Yamabe invariant of the conformal boundary is negative. John M. Lee, The Spectrum of an Asymptotically Hyperbolic Einstein Manifold, Communications in Analysis and Geometry 3 (1995) 253-271, arXiv:dg-ga/9409003v1. 7/15

  8. Brane Productions Example: D3 brane probe in (4+1)-dimensional Asymptotically AdS Space. 8/15

  9. Brane Productions Recall that: 9/15

  10. Brane Productions Spontaneous fragmentation of topological black holes Jose L. F. Barbon, Javier Martinez-Magan 10/15

  11. Brane Productions 11/15

  12. Comparison with Schwinger Effect 12/15

  13. Comparison with Schwinger Effect Production rate: 13/15

  14. Stringy Effects in AdS • Seiberg-Witten Instability Seiberg-Witten action and Instability. Instabilities arise if S becomes negative: large branes have energy which is unbounded from below as they approach the boundary. Brane nucleation.BPSCase:

  15. Seiberg-Witten Instability Seiberg-Witten action is monotonically negative at large r is equivalent to boundary with negative scalar curvature, which implies instability of field theory on the boundary. 15/15

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