Quantum noncommutative gravity in two dimensions |
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Affiliation: | 1. National Research Council Institute for Biodiagnostics, Magnetic Resonance Technology, 435 Ellice Avenue, Winnipeg, MB R3B 1Y6, Canada;2. Alberta Innovates Technology Futures, 435 Ellice Avenue, Winnipeg, MB R3B 1Y6, Canada;3. Biopsychology Program, Department of Psychology, University of Winnipeg, 515 Portage Avenue, Winnipeg, MB R3B 2E9, Canada;4. National Research Council Aquatic and Crop Resource Development, 435 Ellice Avenue, Winnipeg, MB R3B 1Y6, Canada;5. Multimodal and Functional Imaging Group, Central Europe Institute of Technology, Kamenice 753, Brno CZ-62500, Czech Republic;1. School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, United Kingdom;2. Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands;1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;2. College of Mathematics and Information Sciences, Henan University, Kaifeng 475001, China;3. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;4. School of Science, Qilu University of Technology, Jinan 250353, China;5. Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing 100048, China;6. Institute of Mathematics and Interdisciplinary Science, Capital Normal University, Beijing 100048, China |
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Abstract: | We study quantisation of noncommutative gravity theories in two dimensions (with noncommutativity defined by the Moyal star product). We show that in the case of noncommutative Jackiw–Teitelboim gravity the path integral over gravitational degrees of freedom can be performed exactly even in the presence of a matter field. In the matter sector, we study possible choices of the operators describing quantum fluctuations and define their basic properties (e.g., the Lichnerowicz formula). Then we evaluate two leading terms in the heat kernel expansion, calculate the conformal anomaly and the Polyakov action (as an expansion in the conformal field). |
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