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arXiv · 2607.18120

(1,k) CFT and RH problem with the c=-2 case

Mikhail Bershtein·Andrei Grigorev·Anton Shchechkin
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Abstract

Following approach of Iorgov--Lisovyy--Teschner, we construct solutions of the (modified) Riemann--Hilbert problem using conformal blocks of $(1,k)$ Virasoro models. For $k>1$ case, the solution of this Riemann--Hilbert problem is not unique due to more singular behavior at punctures. On the CFT side the dimension of the space of conformal blocks also increases. We specifically study the $k=2$ case, which corresponds to the central charge $c=-2$ and symplectic fermions. We explicitly construct a corresponding solution of the modified Riemann--Hilbert problem in the case of 3 punctures and prove its uniqueness under suitable initial data conditions. We also obtain new bilinear relations for $c=-2$ tau functions.

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Mikhail Bershtein, Andrei Grigorev, Anton Shchechkin. 2026-07-20. (1,k) CFT and RH problem with the c=-2 case. https://arxiv.org/abs/2607.18120

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