2D quantum gravity on compact Riemann surfaces with non-conformal matter

Abstract

We study the gravitational action induced by coupling two-dimensional non-conformal, massive matter to gravity on a compact Riemann surface. We express this gravitational action in terms of finite and well-defined quantities for any value of the mass. A small-mass expansion gives back the Liouville action in the massless limit, the Mabuchi and Aubin-Yau actions to first order, as well as an infinite series of higher-order contributions written in terms of purely geometric quantities.

15 pages, minor corrections

References in corpus (1)

• Lectures on Stability and Constant Scalar Curvature

Cited by in corpus (8)

• String Field Theory -- A Modern Introduction
• 2D gravitational Mabuchi action on Riemann surfaces with boundaries
• BRST cohomology of timelike Liouville theory
• Minisuperspace computation of the Mabuchi spectrum
• Gravitational action for a massive Majorana fermion in 2d quantum gravity
• A short note on dynamics and degrees of freedom in $2d$ classical gravity
• Effective gravitational action for 2D massive fermions
• Effective gravitational action for 2D massive Majorana fermions on arbitrary genus Riemann surfaces