2D gravitational Mabuchi action on Riemann surfaces with boundaries

• Main Authors: Adel Bilal, Corinne de Lacroix
• Format: Article
• Language: English
• Published: SpringerOpen 2017-11-01
• Series: Journal of High Energy Physics
• Subjects: 2D Gravity; Models of Quantum Gravity
• Online Access: http://link.springer.com/article/10.1007/JHEP11(2017)154

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.