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

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.

Cite

BibTeX RIS

BibTeX

@misc{bershtein2026problem,
  title = {{(1,k) CFT and RH problem with the c=-2 case}},
  author = {Mikhail Bershtein and Andrei Grigorev and Anton Shchechkin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.18120},
  eprint = {2607.18120},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.18120},
}

RIS

TY  - UNPB
TI  - (1,k) CFT and RH problem with the c=-2 case
AU  - Mikhail Bershtein
AU  - Andrei Grigorev
AU  - Anton Shchechkin
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2607.18120
UR  - https://arxiv.org/abs/2607.18120
AB  - 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.
ER  -