Irregular Liouville correlators and connection formulae for Heun functions

Abstract

We perform a detailed study of a class of irregular correlators in Liouville Conformal Field Theory, of the related Virasoro conformal blocks with irregular singularities and of their connection formulae. Upon considering their semi-classical limit, we provide explicit expressions of the connection matrices for the Heun function and a class of its confluences. Their calculation is reduced to concrete combinatorial formulae from conformal block expansions.

61 pages, many diagrams, 2 figures, huge list of symbols, comments welcome

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