Complex Gaussian multiplicative chaos
Hubert Lacoin, R\'emi Rhodes, Vincent Vargas
TL;DR
This paper develops a comprehensive theory for complex Gaussian multiplicative chaos, including renormalization and limits, with applications to 2D string theory and Liouville Quantum Gravity.
Contribution
It introduces a rigorous framework for complex Gaussian multiplicative chaos, extending to all dimensions and connecting to string theory and quantum gravity.
Findings
Established a renormalization theory for complex Gaussian chaos
Derived the KPZ formula for Tachyon fields in Liouville Quantum Gravity
Provided a mathematical definition of Tachyon fields in 2D string theory
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.
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