| _version_ | 1866901151544246272 |
|---|---|
| author | Culm Macaday, Sean Eric |
| author_facet | Culm Macaday, Sean Eric |
| contents | <p>We show that the cotangent bundle of Teichmüller space T (Σ_g) — Moncrief's reduced phase space for (2+1) vacuum gravity — arises by symplectic reduction of the zero-enstrophy coadjoint orbit of the corner symmetry group Diff(S) ⋉ SL(2,ℝ)^S by SDiff(S). The zero-enstrophy condition (vanishing normal bundle curvature K⊥) decouples the codimension-2 Codazzi equations, producing holomorphic quadratic differentials as the cotangent fiber. The Ricci equation forces the two normal-direction differentials to be real-proportional at all genera, by the open mapping theorem. The symplectic structure is verified via the Chern-Simons triangle: the corner symplectic potential, restricted to flat normal connections and reduced by SDiff, reproduces the canonical symplectic form on T up to the gravitational normalisation 1/(8πG). This connects the canonical reduction programme for (2+1) gravity with the coadjoint orbit classification of gravitational edge modes, identifying Moncrief's phase space as a distinguished orbit with maximally large little group.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19738589 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Moncrief's Reduced Phase Space from Symplectic Reduction of the Corner Symmetry Group Culm Macaday, Sean Eric general relativity corner symmetry coadjoint orbits Teichmüller space <p>We show that the cotangent bundle of Teichmüller space T (Σ_g) — Moncrief's reduced phase space for (2+1) vacuum gravity — arises by symplectic reduction of the zero-enstrophy coadjoint orbit of the corner symmetry group Diff(S) ⋉ SL(2,ℝ)^S by SDiff(S). The zero-enstrophy condition (vanishing normal bundle curvature K⊥) decouples the codimension-2 Codazzi equations, producing holomorphic quadratic differentials as the cotangent fiber. The Ricci equation forces the two normal-direction differentials to be real-proportional at all genera, by the open mapping theorem. The symplectic structure is verified via the Chern-Simons triangle: the corner symplectic potential, restricted to flat normal connections and reduced by SDiff, reproduces the canonical symplectic form on T up to the gravitational normalisation 1/(8πG). This connects the canonical reduction programme for (2+1) gravity with the coadjoint orbit classification of gravitational edge modes, identifying Moncrief's phase space as a distinguished orbit with maximally large little group.</p> |
| title | Moncrief's Reduced Phase Space from Symplectic Reduction of the Corner Symmetry Group |
| topic | general relativity corner symmetry coadjoint orbits Teichmüller space |
| url | https://doi.org/10.5281/zenodo.19738589 |