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We briefly include here a recent application of spectral networks by Hao and Neitzke (A new construction of \(c = 1\) Virasoro blocks, 2024), namely the non-abelianization of conformal blocks. Hao and Neitzke produce a passage between Virasoro conformal blocks at \(c=1\) on a Riemann surface C and Heisenberg conformal blocks over a double cover of C. The construction builds upon Zamolodchikov’s branched free-field construction (Zamolodchikov, Nucl Phys B 285:481–503, 1987), yet the normalized correlation functions involved now are everywhere regular, thus no additional insertions of Virasoro primary fields have to be considered.

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Non-abelianization for Conformal Virasoro Blocks

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  • 出版模式：

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  • 发表日期：

    2026年

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  • Clarence Kineider,
  • Georgios Kydonakis,
  • Eugen Rogozinnikov,
  • Valdo Tatitscheff,
  • Alexander Thomas

摘要

We briefly include here a recent application of spectral networks by Hao and Neitzke (A new construction of \(c = 1\) Virasoro blocks, 2024), namely the non-abelianization of conformal blocks. Hao and Neitzke produce a passage between Virasoro conformal blocks at \(c=1\) on a Riemann surface C and Heisenberg conformal blocks over a double cover of C. The construction builds upon Zamolodchikov’s branched free-field construction (Zamolodchikov, Nucl Phys B 285:481–503, 1987), yet the normalized correlation functions involved now are everywhere regular, thus no additional insertions of Virasoro primary fields have to be considered.