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.
Article PDF
Similar content being viewed by others
References
A.M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B 103 (1981) 207 [INSPIRE].
T. Mabuchi, K-energy maps integrating Futaki invariants, Tôhuku Math. J. 38 (1986) 575.
T. Mabuchi, Some symplectic geometry on compact Kähler manifolds, Osaka J. Math. 24 (1987) 227.
S. Semmes, Complex Monge-Ampère and symplectic manifolds, Amer. J. Math. 114 (1992) 495.
D.H. Phong and J. Sturm, Lectures on stability and constant scalar curvature, arXiv:0801.4179.
F. Ferrari, S. Klevtsov and S. Zelditch, Gravitational actions in two dimensions and the Mabuchi functional, Nucl. Phys. B 859 (2012) 341 [arXiv:1112.1352] [INSPIRE].
A. Bilal, F. Ferrari and S. Klevtsov, 2D quantum gravity at one loop with Liouville and Mabuchi actions, Nucl. Phys. B 880 (2014) 203 [arXiv:1310.1951] [INSPIRE].
A. Bilal and L. Leduc, Liouville and Mabuchi quantum gravity at two and three loops, to appear.
A. Bilal and F. Ferrari, Multi-loop zeta function regularization and spectral cutoff in curved spacetime, Nucl. Phys. B 877 (2013) 956 [arXiv:1307.1689] [INSPIRE].
E.P. Verlinde and H.L. Verlinde, Multiloop calculations in covariant superstring theory, Phys. Lett. B 192 (1987) 95 [INSPIRE].
E.P. Verlinde and H.L. Verlinde, Chiral bosonization, determinants and the string partition function, Nucl. Phys. B 288 (1987) 357 [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1606.01901
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Bilal, A., Leduc, L. 2D quantum gravity on compact Riemann surfaces with non-conformal matter. J. High Energ. Phys. 2017, 89 (2017). https://doi.org/10.1007/JHEP01(2017)089
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2017)089