Liouville quantum gravity on complex tori

DOI10.1063/1.4938107zbMath1362.81082arXiv1504.00625OpenAlexW1669071243MaRDI QIDQ2795550

Rémi Rhodes, Vincent Vargas, François David

Publication date: 21 March 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.00625

zbMATH Keywords

complex toriGaussian multiplicative chaosLiouville Quantum Gravity

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Quantum field theory on curved space or space-time backgrounds (81T20) Gravitational interaction in quantum theory (81V17) Quantization of the gravitational field (83C45) Path integrals in quantum mechanics (81S40) Anomalies in quantum field theory (81T50)

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Cites Work

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• Liouville quantum gravity on the Riemann sphere
• On Gaussian multiplicative chaos
• Roaming moduli space using dynamical triangulations
• Critical Gaussian multiplicative chaos: convergence of the derivative martingale
• Gaussian multiplicative chaos and applications: a review
• Elliptic functions, Green functions and the mean field equations on tori
• Scaling limits for random quadrangulations of positive genus
• Conformal field theory
• The topology of scaling limits of positive genus random quadrangulations
• Gaussian multiplicative chaos revisited
• The structure of unicellular maps, and a connection between maps of positive genus and planar labelled trees
• The asymptotic number of rooted maps on a surface
• Evaluation of the one loop string path integral
• Quantum field theory techniques in graphical enumeration
• Liouville quantum gravity on the unit disk
• Planar diagrams
• Renormalization of critical Gaussian multiplicative chaos and KPZ relation
• Tightness of the recentered maximum of log-correlated Gaussian fields
• SLE and the free field: Partition functions and couplings
• Tessellations of random maps of arbitrary genus
• Dimers and families of Cauchy-Riemann operators I
• Lattice Sums Then and Now

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