Holographic Uniformization

TL;DR

This paper derives supergravity BPS flow equations for branes wrapping a Riemann surface, revealing geometric flows that interpolate between arbitrary UV metrics and constant-curvature IR metrics, with a rigorous proof of global existence.

Contribution

It introduces novel geometric flow equations on Riemann surfaces within supergravity and proves their solutions interpolate between arbitrary UV and constant IR metrics.

Findings

Existence of solutions interpolating between arbitrary UV and constant IR metrics.

Derivation of supergravity BPS flow equations as geometric flows.

Rigorous proof of global existence of these solutions.

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 UV and the constant-curvature metric in the IR. We confirm this conjecture with a rigorous global existence proof.