2 + 1 dimensional gravity as an exactly soluble system |
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Institution: | 1. Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, 141980 Russia;2. Al-Farabi Kazakh National University, Almaty, 050040 Kazakhstan;3. L.N. Gumilyov Eurasian National University, Nur-Sultan, 010008 Kazakhstan;1. Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Prague 186 75, Czech Republic;2. Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, Prague 115 67, Czech Republic |
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Abstract: | By disentangling the hamiltonian constraint equations, 2 + 1 dimensional gravity (with or without a cosmological constant) is shown to be exactly soluble at the classical and quantum levels. Indeed, it is closely related to Yang-Mills theory with purely the Chern-Simons action, which recently has turned out to define a soluble quantum field theory. 2 + 1 dimensional gravity has a straightforward renormalized perturbation expansion, with vanishing beta function. 2 + 1 dimensional quantum gravity may provide a testing ground for understanding the role of classical singularities in quantum mechanics, may be related to the discrete series of Virasoro representations in 1 + 1 dimensions, and may be a useful tool in studying three-dimensional geometry. |
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