Stress-Energy in Liouville Conformal Field Theory

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http://hdl.handle.net/10138/318559

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Kupiainen , A & Oikarinen , J 2020 , ' Stress-Energy in Liouville Conformal Field Theory ' , Journal of Statistical Physics , vol. 180 , no. 1-6 , pp. 1128-1166 . https://doi.org/10.1007/s10955-020-02601-4

Title: Stress-Energy in Liouville Conformal Field Theory
Author: Kupiainen, Antti; Oikarinen, Joona
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2020-09
Language: eng
Number of pages: 39
Belongs to series: Journal of Statistical Physics
ISSN: 0022-4715
URI: http://hdl.handle.net/10138/318559
Abstract: We construct the stress-energy tensor correlation functions in probabilistic Liouville conformal field theory (LCFT) on the two-dimensional sphere S-2 by studying the variation of the LCFT correlation functions with respect to a smooth Riemannian metric on S-2. In particular we derive conformal Ward identities for these correlation functions. This forms the basis for the construction of a representation of the Virasoro algebra on the canonical Hilbert space of the LCFT. In Kupiainen et al. (Commun Math Phys 371:1005-1069, 2019) the conformal Ward identities were derived for one and two stress-energy tensor insertions using a different definition of the stress-energy tensor and Gaussian integration by parts. By defining the stress-energy correlation functions as functional derivatives of the LCFT correlation functions and using the smoothness of the LCFT correlation functions proven in Oikarinen (Ann Henri Poincare 20(7):2377-2406, 2019) allows us to control an arbitrary number of stress-energy tensor insertions needed for representation theory.
Subject: Liouville model
Conformal field theory
Ward identities
Stress-energy tensor
GAUSSIAN MULTIPLICATIVE CHAOS
QUANTUM
111 Mathematics
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