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SUMMARY:Liouville conformal field theory and the DOZZ formula (1/4)
DTSTART;VALUE=DATE-TIME:20171122T130000Z
DTEND;VALUE=DATE-TIME:20171122T150000Z
DTSTAMP;VALUE=DATE-TIME:20210510T015616Z
UID:indico-event-2806@indico.math.cnrs.fr
DESCRIPTION:\nLiouville conformal field theory (LCFT hereafter)\, introduc
ed by Polyakov in his 1981 seminal work "Quantum geometry of bosonic strin
gs"\, can be seen as a random version of the theory of Riemann surfaces. L
CFT appears in Polyakov's work as a 2d version of the Feynman path integra
l with an exponential interaction term. Since then\, LCFT has emerged in a
wide variety of contexts in the physics literature and in particular rece
ntly in relation with 4d supersymmetric gauge theories (via the AGT conjec
ture). \n\n \n\n\nA major issue in theoretical physics was to solve the
theory\, namely compute the correlation functions. In this direction\, an
intriguing formula for the three point correlations of LCFT was proposed
in the middle of the 90's by Dorn-Otto and Zamolodchikov-Zamolodchikov\, t
he celebrated DOZZ formula. \n\n \n\nThe purpose of the course is twofo
ld (based on joint works with F. David\, A. Kupiainen and R. Rhodes). Firs
t\, I will present a rigorous probabilistic construction of Polyakov's pat
h integral formulation of LCFT. The construction is based on the Gaussian
Free Field. Second\, I will show that the three point correlation function
s of the probabilistic construction indeed satisfy the DOZZ formula. This
establishes an explicit link between probability theory (or statistical ph
ysics) and the so-called conformal bootstrap approach of LCFT.\n\nhttps://
indico.math.cnrs.fr/event/2806/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/2806/
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