Liouville Conformal Field Theory on even-dimensional spheres
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866917696667385856 |
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| author | Cerclé, Baptiste |
| author_facet | Cerclé, Baptiste |
| contents | Initiated by Polyakov in his 1981 seminal work, the study of two-dimensional Liouville Conformal Field Theory has drawn considerable attention over the past decades. Recent progress in the understanding of conformal geometry in dimension higher than two have naturally led to a generalization of Polyakov formalism to higher dimensions, based on conformally invariant operators: Graham-Jenne-Mason-Sparling operators and the $\mathcal{Q}$-curvature.
This document is dedicated to providing a rigorous construction of Liouville Conformal Field Theory on even-dimensional spheres. This is done at the classical level in terms of a generalized \textit{Uniformization} problem, and at the quantum level thanks to a probabilistic construction based on log-correlated fields and Gaussian Multiplicative Chaos. The properties of the objects thus defined are in agreement with the ones expected in the physics literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1912_09219 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Liouville Conformal Field Theory on even-dimensional spheres Cerclé, Baptiste Probability Mathematical Physics 60D05, 81T20, 81T40 Initiated by Polyakov in his 1981 seminal work, the study of two-dimensional Liouville Conformal Field Theory has drawn considerable attention over the past decades. Recent progress in the understanding of conformal geometry in dimension higher than two have naturally led to a generalization of Polyakov formalism to higher dimensions, based on conformally invariant operators: Graham-Jenne-Mason-Sparling operators and the $\mathcal{Q}$-curvature. This document is dedicated to providing a rigorous construction of Liouville Conformal Field Theory on even-dimensional spheres. This is done at the classical level in terms of a generalized \textit{Uniformization} problem, and at the quantum level thanks to a probabilistic construction based on log-correlated fields and Gaussian Multiplicative Chaos. The properties of the objects thus defined are in agreement with the ones expected in the physics literature. |
| title | Liouville Conformal Field Theory on even-dimensional spheres |
| topic | Probability Mathematical Physics 60D05, 81T20, 81T40 |
| url | https://arxiv.org/abs/1912.09219 |