2026/07/20 by Mikhail Bershtein, Andrei Grigorev, Anton Shchechkin
Mathematics · #math-ph #hep-th #math.MP
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.