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Jun 17, 2021 · Polyakov’s Liouville field theory is one such example. Gravity’s Field The Liouville field, which is based on an equation from complex analysis developed in the 1800s by the French mathematician Joseph Liouville, describes a completely random two-dimensional surface — that is, a surface, like Earth’s crust, but one in which the height of every point is chosen randomly.
Feb 3, 2016 · 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 PSL $${_2(\\mathbb{C})}$$ 2 ( C ) -action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly formula. We also make precise conjectures about the relationship ...
- François David, Antti Kupiainen, Rémi Rhodes, Vincent Vargas
- 2016
Apr 17, 2009 · Duality and the Knizhnik-Polyakov-Zamolodchikov Relation in Liouville Quantum Gravity Bertrand Duplantier and Scott Sheffield Phys. Rev. Lett. 102 , 150603 – Published 17 April 2009
- Bertrand Duplantier, Scott Sheffield
- 2009
An introduction to the semi-classical theory for the Polyakov’s functional integral approach to the quantum Liouville theory is presented with the emphasis on geometrical setup and interrelations between the Fuchsian uniformization of Riemann Surfaces and the complex geometry of Teichmüller, Schottky and moduli spaces.
- Leon Takhtajan
- 1992
In this article, we present the Liouville field theory, which was introduced in the eighties in physics by Polyakov as a model for fluctuating metrics in 2D quantum gravity, and outline recent mathematical progress in its study. In particular, we explain the probabilistic construction of this theory carried out by David–Kupiainen–Rhodes ...
) etc. [21]-[22]. Soviet scientist A.M. Polyakov, known for a number of fundamental contributions to quantum field theory, found a new use for the equation (L e) in high energy physics, in the quantum geometry of bosonic strings [35]: indeed, the equation of motion associated with the so-called “Liouville action” 𝑆[𝜑]=𝐶∫(1 2 ...
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Aug 30, 2004 · A step in this direction was done in our previous paper [20] where we constructed the classical Liouville action satisfying the Polyakov conjecture in the case of hyperbolic singularities. In the present paper we calculate the classical Liouville action for three hyperbolic singularities and show that the result agrees with the classical limit of the corresponding DOZZ three-point function.
