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Topology of future infinity in dS/CFT

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Abstract

The dS/CFT proposal of Anninos, Hartman, and Strominger relates quantum Vasiliev gravity in dS4 to a large N vector theory in three dimensions. We use this proposal to compute the Wheeler-de Witt wave function of a universe having a particular topology at future infinity. This amplitude is found to grow rapidly with the topological complexity of the spatial slice; this is due to the plethora of states of the Chern-Simons theory that is needed to impose the singlet constraint. Various mechanisms are considered which might ameliorate this growth, but none seems completely satisfactory. We also study the topology dependence in Einstein gravity by computing the action of complex instantons; the wave function then depends on a choice of contour through the space of metrics. The most natural contour prescription leads to a growth with genus similar to the one found in Vasiliev theory, albeit with a different power of Newton’s constant.

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Authors and Affiliations

  1. Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA, 94305, U.S.A.

    Shamik Banerjee, Ðorđe Radičević & Stephen Shenker

  2. Physics Department, McGill University, 3600 Rue University, Montréal, QC H3A 2T8, Canada

    Alexandre Belin, Arnaud Lepage-Jutier & Alexander Maloney

  3. Kavli IPMU (WPI), The University of Tokyo, Kashiwa, Chiba, 277-8583, Japan

    Simeon Hellerman

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  1. Shamik Banerjee
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  2. Alexandre Belin
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  3. Simeon Hellerman
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  4. Arnaud Lepage-Jutier
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  5. Alexander Maloney
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  6. Ðorđe Radičević
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  7. Stephen Shenker
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Correspondence to Ðorđe Radičević.

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ArXiv ePrint: 1306.6629

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Banerjee, S., Belin, A., Hellerman, S. et al. Topology of future infinity in dS/CFT. J. High Energ. Phys. 2013, 26 (2013). https://doi.org/10.1007/JHEP11(2013)026

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