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## Crossing invariant correlation functions at c = 1 from isomonodromic τ functions

Journal of High Energy Physics. 2019. Vol. 2019. No. 11. P. 1-36.
Gavrylenko P., Santachiara R.

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 $${\mathcal{M}}_{0,4}^{\mathrm{SL}\left(s,\mathbb{C}\right)}$$ of SL(2, 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.