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SUMMARY:Liouville conformal field theory and the DOZZ formula (2/4)
DTSTART;VALUE=DATE-TIME:20171124T093000Z
DTEND;VALUE=DATE-TIME:20171124T113000Z
DTSTAMP;VALUE=DATE-TIME:20190418T211452Z
UID:indico-event-2807@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\ncA major issue in theoretical physics was to solve the theo
ry\, namely compute the correlation functions. In this direction\, an intr
iguing formula for the three point correlations of LCFT was proposed in th
e middle of the 90's by Dorn-Otto and Zamolodchikov-Zamolodchikov\, the ce
lebrated DOZZ formula. \n\n \n\nThe purpose of the course is twofold (bas
ed on joint works with F. David\, A. Kupiainen and R. Rhodes). First\, I w
ill present a rigorous probabilistic construction of Polyakov's path integ
ral formulation of LCFT. The construction is based on the Gaussian Free Fi
eld. Second\, I will show that the three point correlation functions of th
e probabilistic construction indeed satisfy the DOZZ formula. This establi
shes an explicit link between probability theory (or statistical physics)
and the so-called conformal bootstrap approach of LCFT.\n\nhttps://indico.
math.cnrs.fr/event/2807/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/2807/
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