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Corpus ID: 245634492

Segal's axioms and bootstrap for Liouville Theory

@inproceedings{Guillarmou2021SegalsAA,
title={Segal's axioms and bootstrap for Liouville Theory},
author={Colin Guillarmou and Antti Kupiainen and R{\'e}mi Rhodes and Vincent Vargas},
year={2021}
}

In 1987 Graeme Segal gave a functorial definition of Conformal Field Theory (CFT) that was designed to capture the mathematical essence of the Conformal Bootstrap formalism pioneered in physics by Belavin-Polyakov-Zamolodchikov. In Segal's formulation the basic objects of CFT, the correlation functions of conformal primary fields, are viewed as functions on the moduli space of Riemann surfaces with marked points which behave naturally under gluing of surfaces. In this paper we give a… Expand

Toda Conformal Field Theories (CFTs) form a family of 2d CFTs indexed by semisimple and complex Lie algebras. They are natural generalizations of the Liouville CFT in that they enjoy an enhanced… Expand

. We obtain exact formulae for three basic quantities in random conformal geometry that depend on the modulus of an annulus. The ﬁrst is for the law of the modulus of the Brownian annulus describing… Expand

Given 2n unit equilateral triangles, there are finitely many ways to glue each edge to a partner. We obtain a random sphere-homeomorphic surface by sampling uniformly from the gluings that produce a… Expand

We study a class of random permutons which can be constructed from a pair of space-ﬁlling Schramm-Loewner evolution (SLE) curves on a Liouville quantum gravity (LQG) surface. This class includes the… Expand

In this note, we give a unified rigorous construction for the Liouville conformal field theory on compact Riemann surface with boundaries for γ ∈ (0, 2] and prove a certain type of Markov property.… Expand