$\mathrm{SL}(2,\mathbb{R})$ Gauge Theory, Hyperbolic Geometry and Virasoro Coadjoint Orbits

Matthias Blau, Donald R. Youmans

It has long been known that the moduli space of hyperbolic metrics on the disc can be identified with the Virasoro coadjoint orbit $\mathrm{Diff}^+(S^1) / \mathrm{SL}(2,\mathbb{R})…