Proof of Polyakov conjecture for general elliptic singularities

DOI10.1016/S0370-2693(01)00998-4zbMath0980.83036arXivhep-th/0105081OpenAlexW1973276612WikidataQ123159345 ScholiaQ123159345MaRDI QIDQ5942958

Luigi Cantini, Domenico Seminara, Pietro Menotti

Publication date: 16 September 2001

Published in: Physics Letters. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/0105081

zbMATH Keywords

\((2+1)\)-dimensional gravity\(SU(1,1)\) Riemann-Hilbert problemRiemann sphere

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Relativistic gravitational theories other than Einstein's, including asymmetric field theories (83D05) Analogues of general relativity in lower dimensions (83C80)

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Liouville theory and uniformization of four-punctured sphere ⋮ Hyperbolic 2-spheres with conical singularities, accessory parameters and Kähler metrics on ℳ_{0,𝓃} ⋮ Liouville theory, \( \mathcal{N} = 2 \) gauge theories and accessory parameters ⋮ Semiclassical and quantum Liouville theory on the sphere ⋮ Classical geometry from the quantum Liouville theory ⋮ Semiclassical limit of the FZZT Liouville theory ⋮ Determinants of Laplacians for constant curvature metrics with three conical singularities on the 2-sphere ⋮ Polyakov conjecture for hyperbolic singularities ⋮ Irregular Liouville correlators and connection formulae for Heun functions ⋮ \(T\overline{T}\) deformation of classical Liouville field theory ⋮ Classical conformal blocks from TBA for the elliptic Calogero-Moser system ⋮ Hyperbolic three-string vertex ⋮ Torus classical conformal blocks ⋮ Supersymmetric Gauge Theories, Quantization of $${\mathcal M}_\mathrm{flat}$$ , and Conformal Field Theory ⋮ Accessory parameters for Liouville theory on the torus ⋮ Hyperbolic deformation of the strip-equation and the accessory parameters for the torus ⋮ The Kähler potential of Abelian Higgs vortices ⋮ Liouville theory, accessory parameters and \((2+1)\)-dimensional gravity ⋮ The continuation method and the real analyticity of the accessory parameters: the parabolic case

Cites Work

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• ADM approach to \(2+1\) dimensional gravity
• Explicit solutions for point particles and black holes in spaces of constant curvature in \(2+1-D\) gravity
• EQUIVALENCE OF GEOMETRIC h<1/2 AND STANDARD c>25 APPROACHES TO TWO-DIMENSIONAL QUANTUM GRAVITY
• Prescribing Curvature on Compact Surfaces with Conical Singularities
• Uniformisation of the twice–punctured disc - problems of confluence
• Accessory Parameters for Punctured Spheres
• Several Complex Variables and the Geometry of Real Hypersurfaces

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