The paper derives the modular connection constant for tau functions on the one-punctured torus and obtains an exact closed formula for the c=1 Virasoro modular kernel.
Painlev\'e/CFT correspondence on a torus
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abstract
This note details the relationship between the isomonodromic tau-function and conformal blocks, on a torus with one simple pole. It is based on the author's talk at ICMP 2021.
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Modular transformations of tau functions and conformal blocks on the torus
The paper derives the modular connection constant for tau functions on the one-punctured torus and obtains an exact closed formula for the c=1 Virasoro modular kernel.