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SUMMARY:Conformal bootstrap and statistical models
DTSTART;VALUE=DATE-TIME:20210503T070000Z
DTEND;VALUE=DATE-TIME:20210528T160000Z
DTSTAMP;VALUE=DATE-TIME:20200926T060000Z
UID:indico-event-5833@indico.ijclab.in2p3.fr
DESCRIPTION:A platform where experts in conformal bootstrap techniques and
in statistical physics can discuss and solve specific mathematical and ph
ysical problems. \n\nWeek 1: Status of the conformal bootstrap\n\nLeading
experts on the conformal bootstrap will give introductory courses on:\n\n\
n Conformal symmetry and conformally invariant QFTs.\n Input and output da
ta of the conformal bootstrap.\n Analytical and numerical tools.\n Pros an
d cons of various techniques.\n\n\nWeek 2: Statistical physics targets\n\n
Discussing various statistical models\, with an emphasis on the aspects th
at are relevant to a bootstrap approach.\n\n\n Symmetries\, unitarity.\n S
pace of states\, critical exponents\, correlation functions.\n Which obser
vables can be computed with a good precision?\n Families of models\, margi
nal deformations\, toy models.\n Outstanding physical questions\, interest
of the critical limit for these questions.\n\n\nExamples may include: per
colation\, depinning\, loop-erased random walks\, sandpiles\, Chalker-Codd
ington network for the integer quantum Hall effect.\n\nWeek 3: Bootstrap f
or structural phase transitions\n\nStructural phase transitions are descri
bed by unitary theories\, which makes them accessible to existing numerica
l bootstrap methods. However\, they are challenging because of their intri
cate group theory and phenomenology. First we will review:\n\n\n Necessary
group theory tools.\n Main results from the renormalization group approac
h.\n Experimental situation.\n\n\nThen we will apply the bootstrap approac
h.\n\nWeek 4: Non-unitary bootstrap methods\n\nThe best-developed numerica
l bootstrap techniques rely on unitarity\, which is however not available
in logarithmic CFTs\, the critical Potts model\, percolation\, or disorder
ed systems. We will explore two approaches to the non-unitary bootstrap:\n
\n\n The perturbative epsilon expansion.\n Gliozzi's method and extremal f
lows.\n\n\nWe may start with a family of unitary models such as the O(N) m
odel\, and vary the parameter continuously to a non-unitary or logarithmic
fixed point.\n\n\n\nhttps://indico.ijclab.in2p3.fr/event/5833/
LOCATION:Institut Pascal\, Orsay\, France
URL:https://indico.ijclab.in2p3.fr/event/5833/
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