Fractional vertex-operator correlations of the massless sine-Gordon model at β = 4π are shown to equal Palmer's tau functions of massive twisted Dirac operators, giving a proof of the Lukyanov-Zamolodchikov one-point formula.
On the regularity of complex multiplicative chaos
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abstract
Denote by $\mu_\beta="\exp(\beta X)"$ the Gaussian multiplicative chaos which is defined using a log-correlated Gaussian field $X$ on a domain $U\subset\mathbb{R}^d$. The case $\beta\in\mathbb{R}$ has been studied quite intensively, and then $\mu_\beta$ is a random measure on $U$. It is known that $\mu_\beta$ can also be defined for complex values $\beta$ lying in certain subdomain of $\mathbb{C}$, and then the realizations of $\mu_\beta$ are random generalized functions on $U$. In this note we complement the results of Junnila et al. (where the case of purely imaginary $\beta$ was considered) by studying the Besov-regularity of $\mu_\beta$ and the finiteness of moments for general complex values of $\beta$.
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Twisted Dirac operators and fractional correlations of the massless sine-Gordon model at the free fermion point
Fractional vertex-operator correlations of the massless sine-Gordon model at β = 4π are shown to equal Palmer's tau functions of massive twisted Dirac operators, giving a proof of the Lukyanov-Zamolodchikov one-point formula.