Abstract
We present the manifestly covariant canonical operator formalism of a Weyl invariant (or equivalently, a locally scale invariant) gravity whose classical action consists of the well-known conformal gravity and Weyl invariant scalar-tensor gravity, on the basis of the Becchi-Rouet-Stora-Tyupin (BRST) formalism. It is shown that there exists a Poincaré-like IOSp(8|8) global symmetry as in Einstein’s general relativity, which should be contrasted to the case of only the Weyl invariant scalar-tensor gravity where we have a more extended Poincaré-like IOSp(10|10) global symmetry. This reduction of the global symmetry is attributed to the presence of the Stückelberg symmetry.
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This work is supported in part by the JSPS Kakenhi Grant No. 21K03539.
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Oda, I., Ohta, M. Quantum conformal gravity. J. High Energ. Phys. 2024, 213 (2024). https://doi.org/10.1007/JHEP02(2024)213
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DOI: https://doi.org/10.1007/JHEP02(2024)213