Title:
Semigroups associated to the Gaussian Free Field and application to Conformal Bootstrap
Abstract:
In this talk I will recall the basics related to the 2D Gaussian Free Field (GFF) and explain what is the natural semigroup associated
to this random field from the point of view of quantum mechanics. Then I will perturb this semigroup with an exponential potential and explain
how one can obtain a spectral resolution for the generator by means of scattering theory. The main application is to compute the spectrum of Liouville conformal field theory (LCFT)
and establish the bootstrap formula for the 4 point correlation function of LCFT. This is motivated by the AGT conjecture, which claims that
Nekrasov’s partition function of 4d supersymmetric Yang-Mills is equal to the 4 point correlation function of LCFT.