Liouville Quantum Gravity on the Riemann Sphere

By F. David, A. Kupiainen, Rémi Rhodes, Vincent Vargas. Communications in Mathematical Physics, 2014

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In this paper, we rigorously construct Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov. We establish some of its fundamental properties like conformal covariance under PSL2(C)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${_2(\mathbb{C})}$$\end{document}-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly formula. We also make precise conjectures about the relationship of the theory to scaling limits of random planar maps conformally embedded onto the sphere.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/433b9d2e9ec0ed6dcb8e08873a55a4cb6f616ef7

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Citations in the corpus

The Riemann zeta function and Gaussian multiplicative chaos: Statistics on the critical line (2016, background): “During the last 15 years there has been a new wave of interest in multiplicative chaos, partly due to its important connections to Stochastic Loewner Evolution [82, 4], to quantum gravity and scaling limits of random planar maps [32, 63, 13, 64, 65, 66, 27], as well as to models in finance and turbu”