Complex Gaussian multiplicative chaos

Lacoin, Hubert; Rhodes, Rémi; Vargas, Vincent

Lacoin, Hubert; Rhodes, Rémi; Vargas, Vincent (2015), Complex Gaussian multiplicative chaos, Communications in Mathematical Physics, 337, 2, p. 569-632. 10.1007/s00220-015-2362-4

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1307.6117v3

Date

2015

Journal name

Communications in Mathematical Physics

Volume

337

Number

Publisher

Springer

Published in

Paris

Pages

569-632

Abstract (EN)

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.

Subjects / Keywords

tachyon fields; Random measures; multifractal; Mesures aléatoires