Imaginary multiplicative chaos: different questions from different contexts, and a few answers too

Abstract: Imaginary multiplicative chaos is formally given by exp(iG), where G is a log-correlated Gaussian field in d dimensions. It comes up in several different contexts. For example - as a analytic continuation of the real multiplicative chaos, that is central in the probabilistic study of Liouville quantum gravity and Liouville CFT; - when taking the continuum limit of the spin field for the XOR-Ising model; - in relation to the Kosterlitz-Thouless-type of phase transitions. In this talk I will try to explain how imaginary chaos comes up in these contexts, which questions it brings along, and how to answer some of these questions. This is a joint work with J. Junnila, and also partly with A. Jego.

mathematical physicsprobability

Audience: researchers in the topic

Probability and the City Seminar

Series comments: The Probability and the City Seminar is organized jointly by the probability groups of Columbia University and New York University.

Video recordings of talks are posted online at www.youtube.com/channel/UC0CXjG-ZSIZHy0S40Px2FEQ .