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Journal of High Energy Physics

, 2017:154 | Cite as

2D gravitational Mabuchi action on Riemann surfaces with boundaries

Open Access
Regular Article - Theoretical Physics
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Abstract

We study the gravitational action induced by coupling two-dimensional non-conformal, massive matter to gravity on a Riemann surface with boundaries. A small-mass expansion gives back the Liouville action in the massless limit, while the first-order mass correction allows us to identify what should be the appropriate generalization of the Mabuchi action on a Riemann surface with boundaries. We provide a detailed study for the example of the cylinder. Contrary to the case of manifolds without boundary, we find that the gravitational Lagrangian explicitly depends on the space-point, via the geodesic distances to the boundaries, as well as on the modular parameter of the cylinder, through an elliptic θ-function.

Keywords

2D Gravity Models of Quantum Gravity 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique de l’ École Normale SupérieurePSL Research University, CNRS, Sorbonne Universités, UPMC Paris 6Paris Cedex 05France

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