The paper proves the conifold gap property for Weierstrass elliptic topological recursion and gives an algebraic construction of the rank 5/2 Virasoro Whittaker state, linking the Painlevé I tau function to CFT and holomorphic anomaly approaches.
Connection problem for the tau-function of the Sine-Gordon reduction of Painlev\'{e}-III equation via the Riemann-Hilbert approach
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abstract
We evaluate explicitly, in terms of the Cauchy data, the constant pre-factor in the large $x$ asymptotics of the Painlev\'e III tau-function. Our result proves the conjectural formula for this pre-factor obtained recently by O. Lisovyy, Y. Tykhyy, and the first co-author with the help of the recently discovered connection of the Painlev\'e tau-functions with the Virasoro conformal blocks. Our approach does not use this connection, and it is based on the Riemann-Hilbert method.
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Many-faced Painlev\'e I: irregular conformal blocks, topological recursion, and holomorphic anomaly approaches
The paper proves the conifold gap property for Weierstrass elliptic topological recursion and gives an algebraic construction of the rank 5/2 Virasoro Whittaker state, linking the Painlevé I tau function to CFT and holomorphic anomaly approaches.