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

Abstract

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