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Operator product expansion in two-dimensional quantum gravity
Affiliation:1. National Laboratory for High Energy Physics (KEK), Tsukuba, Ibaraki 305, Japan;2. Department of Physics, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan;1. School of Applied Physics, Faculty of Science and Technology, National University of Malaysia, Selangor, Malaysia;2. Malaysian Nuclear Agency, Selangor, Malaysia;3. Atomic Energy Licensing Board, Selangor, Malaysia;4. RELKO Ltd., Bratislava, Slovak Republic;1. School of Applied Physics, Faculty of Science and Technology, National University of Malaysia, Selangor, Malaysia;2. Malaysian Nuclear Agency, Selangor, Malaysia;3. Atomic Energy Licensing Board, Selangor, Malaysia;1. DEIB, Politecnico di Milano – P.zza L. Da Vinci, 32, 20133, Milano, Italy;2. IEIIT, Consiglio Nazionale delle Ricerche, Italy;1. SUPA School of Physics and Astronomy, University of Glasgow, UK;2. Scottish Universities Environmental Research Centre, East Kilbride, UK
Abstract:We consider correlation functions of operators and the operator product expansion in two-dimensional quantum gravity. First we introduce correlation functions with geodesic distances between operators kept fixed. Next, by making two of the operators closer, we examine whether there exists an analog of the operator product expansion in ordinary field theories. Our results suggest that the operator product expansion holds in quantum gravity as well, though special care should be taken regarding the physical meaning of fixing geodesic distances on a fluctuating geometry.
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