2D Quantum Gravity at One Loop with Liouville and Mabuchi Actions
arXiv:1310.1951 · doi:10.1016/j.nuclphysb.2014.01.005
Abstract
We study a new two-dimensional quantum gravity theory, based on a gravitational action containing both the familiar Liouville term and the Mabuchi functional, which has been shown to be related to the coupling of non-conformal matter to gravity. We compute the one-loop string susceptibility from a first-principle, path integral approach in the Kahler parameterization of the metrics and discuss the particularities that arise in the case of the pure Mabuchi theory. While we mainly use the most convenient spectral cutoff regularization to perform our calculations, we also discuss the interesting subtleties associated with the multiplicative anomaly in the familiar zeta-function scheme, which turns out to have a genuine physical effect for our calculations. In particular, we derive and use a general multiplicative anomaly formula for Laplace-type operators on arbitrary compact Riemann surfaces.
27 pages, minor changes in the abstract and introduction
References in corpus (5)
Cited by in corpus (12)
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- Mabuchi spectrum from the minisuperspace
- 2D gravitational Mabuchi action on Riemann surfaces with boundaries
- BRST cohomology of timelike Liouville theory
- Stability and integration over Bergman metrics
- Minisuperspace computation of the Mabuchi spectrum
- Finite cut-off JT and Liouville quantum gravities on the disk at one loop
- 2D Quantum Gravity on Compact Riemann Surfaces and Two-Loop Partition Function: Circumventing the c=1 Barrier?
- 2D quantum gravity at three loops: a counterterm investigation
- Gravitational action for a massive Majorana fermion in 2d quantum gravity
- Effective gravitational action for 2D massive Majorana fermions on arbitrary genus Riemann surfaces