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SUMMARY:Liouville conformal field theory and the DOZZ formula (3/4)
DTSTART;VALUE=DATE-TIME:20171129T130000Z
DTEND;VALUE=DATE-TIME:20171129T150000Z
DTSTAMP;VALUE=DATE-TIME:20190419T003144Z
UID:indico-event-2808@indico.math.cnrs.fr
DESCRIPTION:Liouville conformal field theory (LCFT hereafter)\, introduced
by Polyakov in his 1981 seminal work "Quantum geometry of bosonic strings
"\, can be seen as a random version of the theory of Riemann surfaces. LCF
T appears in Polyakov's work as a 2d version of the Feynman path integral
with an exponential interaction term. Since then\, LCFT has emerged in a w
ide variety of contexts in the physics literature and in particular recent
ly in relation with 4d supersymmetric gauge theories (via the AGT conjectu
re). \n\n \n\nA major issue in theoretical physics was to solve the theor
y\, namely compute the correlation functions. In this direction\, an intri
guing formula for the three point correlations of LCFT was proposed in the
middle of the 90's by Dorn-Otto and Zamolodchikov-Zamolodchikov\, the cel
ebrated DOZZ formula. \n\n \n\nThe purpose of the course is twofold (base
d on joint works with F. David\, A. Kupiainen and R. Rhodes). First\, I wi
ll present a rigorous probabilistic construction of Polyakov's path integr
al formulation of LCFT. The construction is based on the Gaussian Free Fie
ld. Second\, I will show that the three point correlation functions of the
probabilistic construction indeed satisfy the DOZZ formula. This establis
hes an explicit link between probability theory (or statistical physics) a
nd the so-called conformal bootstrap approach of LCFT.\n\nhttps://indico.m
ath.cnrs.fr/event/2808/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/2808/
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