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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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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DOI: https://doi.org/10.1007/s00220-013-1675-4