2D dilaton gravity and the Weil-Petersson volumes with conical defects

Lorenz Eberhardt; Gustavo J. Turiaci

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arXiv · 2304.14948

2D dilaton gravity and the Weil-Petersson volumes with conical defects

Lorenz Eberhardt·Gustavo J. Turiaci

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Abstract

We derive the Weil-Petersson measure on the moduli space of hyperbolic surfaces with defects of arbitrary opening angles and use this to compute its volume. We conjecture a matrix integral computing the corresponding volumes and confirm agreement in simple cases. We combine this mathematical result with the equivariant localization approach to Jackiw-Teitelboim gravity to justify a proposed exact solution of pure 2d dilaton gravity for a large class of dilaton potentials.

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Lorenz Eberhardt, Gustavo J. Turiaci. 2023-04-28. 2D dilaton gravity and the Weil-Petersson volumes with conical defects. https://arxiv.org/abs/2304.14948

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