Regular Article - Theoretical Physics
Real classical geometry with arbitrary deficit parameter(s) in deformed Jackiw–Teitelboim gravity
Department of Physics, College of Science, Sultan Qaboos University, P.O. Box 36, Al-Khodh 123, Muscat, Sultanate of Oman
Accepted: 16 February 2021
Published online: 1 March 2021
An interesting deformation of Jackiw–Teitelboim (JT) gravity has been proposed by Witten by adding a potential term as a self-coupling of the scalar dilaton field. During calculating the path integral over fields, a constraint comes from integration over as . The resulting Euclidean metric suffered from a conical singularity at . A possible geometry is modeled locally in polar coordinates by . In this letter we show that there exists another family of ”exact” geometries for arbitrary values of the . A pair of exact solutions are found for the case of . One represents the static patch of the AdS and the other one is the non-static patch of the AdS metric. These solutions were used to construct the Green function for the inhomogeneous model with . We address a type of phase transition between different patches of the AdS in theory because of the discontinuity in the first derivative of the metric at . We extended the study to the exact space of metrics satisfying the constraint as a modulus diffeomorphisms for an arbitrary set of deficit parameters . The space is the moduli space of Riemann surfaces of genus g with k conical singularities located at , denoted by .
© The Author(s) 2021
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