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Holographic Uniformization

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Abstract

We derive and study supergravity BPS flow equations for M5 or D3 branes wrapping a Riemann surface. They take the form of novel geometric flows intrinsically defined on the surface. Their dual field-theoretic interpretation suggests the existence of solutions interpolating between an arbitrary metric in the ultraviolet and the constant-curvature metric in the infrared. We confirm this conjecture with a rigorous global existence proof.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794-3651, USA

    Michael T. Anderson

  2. Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY, 11794-3636, USA

    Christopher Beem & Nikolay Bobev

  3. C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY, 11794-3840, USA

    Leonardo Rastelli

Authors
  1. Michael T. Anderson
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  2. Christopher Beem
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  3. Nikolay Bobev
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  4. Leonardo Rastelli
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Correspondence to Christopher Beem.

Additional information

Communicated by N. A. Nekrasov

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Anderson, M.T., Beem, C., Bobev, N. et al. Holographic Uniformization. Commun. Math. Phys. 318, 429–471 (2013). https://doi.org/10.1007/s00220-013-1675-4

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