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Lattice Chern-Simons gravity via the Ponzano-Regge model
Institution:1. Department of Physics, Hokkaido University, Sapporo, 060-0810, Japan;2. Niels Bohr Institute, Blegdamsvj 17, Copenhagen, Denmark;1. Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China;2. School of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China;1. The Unit of Energy Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;2. NRCN, P.O. Box 9001, Beer-Sheva 84190, Israel;3. Department of Materials Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;4. Department of Materials Science and Engineering, Tel Aviv University, Ramat Aviv 69978001, Israel;5. Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;1. Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China;2. University of Chinese Academy of Sciences, Beijing 100049, China;3. Liaoning University, Shenyang 110036, China
Abstract:We propose a lattice version of Chem-Simons gravity and show that the partition function coincides with the Ponzano-Regge model and the action leads to the Chem-Simons gravity in the continuum limit. The action is explicitly constructed by the lattice dreibein and spin connection and is shown to be invariant under lattice local Lorentz transformations and gauge diffeomorphisms. The action includes the constraint which can be interpreted as a gauge fixing condition of the lattice gauge diffeomorphism.
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