Abstract
We compute the gravitational action of a free massive Majorana fermion coupled to two-dimensional gravity on compact Riemann surfaces of arbitrary genus. The structure is similar to the case of the massive scalar. The small-mass expansion of the gravitational yields the Liouville action at zeroth order, and we can identify the Mabuchi action at first order. While the massive Majorana action is a conformal deformation of the massless Majorana CFT, we find an action different from the one given by the David-Distler-Kawai (DDK) ansatz.
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Acknowledgments
We would like to thank Andreas Wipf for useful discussions.
This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 891169. This work is supported by the National Science Foundation under Cooperative Agreement PHY-2019786 (The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, http://iaif i.org/).
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de Lacroix, C., Erbin, H. & Lahoche, V. Gravitational action for a massive Majorana fermion in 2d quantum gravity. J. High Energ. Phys. 2024, 68 (2024). https://doi.org/10.1007/JHEP01(2024)068
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DOI: https://doi.org/10.1007/JHEP01(2024)068