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arXiv · 1812.10362

Crossing invariant correlation functions at $c=1$ from isomonodromic $\tau$ functions

Pavlo Gavrylenko·Raoul Santachiara
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Abstract

We present an approach that gives rigorous construction of a class of crossing invariant functions in $c=1$ CFTs from the weakly invariant distributions on the moduli space $\mathcal M_{0,4}^{SL(2,\mathbb{C})}$ of $SL(2,\mathbb{C})$ flat connections on the sphere with four punctures. By using this approach we show how to obtain correlation functions in the Ashkin-Teller and the Runkel-Watts theory. Among the possible crossing-invariant theories, we obtain also the analytic Liouville theory, whose consistence was assumed only on the basis of numerical tests.

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Pavlo Gavrylenko, Raoul Santachiara. 2018-12-26. Crossing invariant correlation functions at $c=1$ from isomonodromic $\tau$ functions. https://doi.org/10.1007/jhep11(2019)119

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