2D gravitational Mabuchi action on Riemann surfaces with boundaries. (November 2017)

• Record Type: Journal Article
• Authors: Bilal, Adel; Lacroix, Corinne
• Is Part Of: Journal of high energy physics. Volume 11(2017)
• Page Start: 1
• Page End: 35
• Publication Date: 2017-11
• Subjects: 2D Gravity -- Models of Quantum Gravity; Particles (Nuclear physics) -- Periodicals; Particules (Physique nucléaire) -- Périodiques; 539.7605
• DOI: 10.1007/JHEP11(2017)154
• Languages: English
• ISSNs: 1029-8479

Abstract

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 ellipticθ -function.