Complex Gaussian multiplicative chaos
Abstract
In this article, we study complex Gaussian multiplicative chaos. More precisely, we study the renormalization theory and the limit of the exponential of a complex log-correlated Gaussian field in all dimensions (including Gaussian Free Fields in dimension 2). Our main working assumption is that the real part and the imaginary part are independent. We also discuss applications in 2D string theory; in particular we give a rigorous mathematical definition of the so-called Tachyon fields, the conformally invariant operators in critical Liouville Quantum Gravity with a c=1 central charge, and derive the original KPZ formula for these fields.
Keywords
Cite
@article{arxiv.1307.6117,
title = {Complex Gaussian multiplicative chaos},
author = {Hubert Lacoin and Rémi Rhodes and Vincent Vargas},
journal= {arXiv preprint arXiv:1307.6117},
year = {2015}
}
Comments
66 pages, 5 figures, contains open problems and application in 2 dimensional string theory. The new version contains the KPZ formula for the Tachyon fields and further discussions about applications