The unitary conformal field theory behind 2D Asymptotic Safety
| Autor: | Andreas Nink, Martin Reuter |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Physics
High Energy Physics - Theory Nuclear and High Energy Physics 010308 nuclear & particles physics Conformal field theory Asymptotic safety in quantum gravity FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) Mathematical Physics (math-ph) Fixed point String theory 01 natural sciences General Relativity and Quantum Cosmology Gravitation Theoretical physics High Energy Physics::Theory High Energy Physics - Theory (hep-th) 0103 physical sciences Quantum gravity 010306 general physics Central charge Mathematical Physics Induced gravity |
| Zdroj: | Journal of High Energy Physics |
| Popis: | Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in $d>2$ dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge $c=25$. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a complete quenching of the a priori expected Knizhnik-Polyakov-Zamolodchikov (KPZ) scaling. A possible connection of this prediction to Monte Carlo results obtained in the discrete approach to 2D quantum gravity based upon causal dynamical triangulations is mentioned. Similarities of the fixed point theory to, and differences from, non-critical string theory are also described. On the technical side, we provide a detailed analysis of an intriguing connection between the Einstein-Hilbert action in $d>2$ dimensions and Polyakov's induced gravity action in two dimensions. 64 pages |
| Databáze: | OpenAIRE |
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