Renormalizability of Liouville quantum field theory at the Seiberg bound

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David , F , Kupiainen , A , Rhodes , R & Vargas , V 2017 , ' Renormalizability of Liouville quantum field theory at the Seiberg bound ' , Electronic Journal of Probability , vol. 22 , 93 . https://doi.org/10.1214/17-EJP113

Title: Renormalizability of Liouville quantum field theory at the Seiberg bound
Author: David, Francois; Kupiainen, Antti; Rhodes, Remi; Vargas, Vincent
Other contributor: University of Helsinki, Department of Mathematics and Statistics


Date: 2017
Language: eng
Number of pages: 26
Belongs to series: Electronic Journal of Probability
ISSN: 1083-6489
DOI: https://doi.org/10.1214/17-EJP113
URI: http://hdl.handle.net/10138/228566
Abstract: Liouville Quantum Field Theory (LQFT) can be seen as a probabilistic theory of 2d Riemannian metrics e(phi(z)) |dz|(2), conjecturally describing scaling limits of discrete 2d-random surfaces. The law of the random field phi in LQFT depends on weights alpha is an element of R that in classical Riemannian geometry parametrize power law singularities in the metric. A rigorous construction of LQFT has been carried out in [3] in the case when the weights are below the so called Seiberg bound: alpha <Q where Q parametrizes the random surface model in question. These correspond to studying uniformized surfaces with conical singularities in the classical geometrical setup. An interesting limiting case in classical geometry are the cusp singularities. In the random setup this corresponds to the case when the Seiberg bound is saturated. In this paper, we construct LQFT in the case when the Seiberg bound is saturated which can be seen as the probabilistic version of Riemann surfaces with cusp singularities. The construction involves methods from Gaussian Multiplicative Chaos theory at criticality.
Subject: Liouville quantum field theory
Gaussian multiplicative chaos
KPZ formula
Polyakov formula
punctures
cusp singularity
uniformization theorem
GAUSSIAN MULTIPLICATIVE CHAOS
GRAVITY
111 Mathematics
112 Statistics and probability
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