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Complex Gaussian multiplicative chaos

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
2
Publisher
Springer
Published in
Paris
Pages
569-632
Publication identifier
10.1007/s00220-015-2362-4
Metadata
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Author(s)
Lacoin, Hubert
Rhodes, Rémi
Vargas, Vincent
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

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