Liouville Blocks from Spectral Networks
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915962999013376 |
|---|---|
| author | Hollands, Lotte Murugesan, Subrabalan |
| author_facet | Hollands, Lotte Murugesan, Subrabalan |
| contents | In this paper, we investigate the role of spectral networks in quantum Liouville theory, with particular emphasis on spectral networks of Fenchel-Nielsen-type. In the first part, we construct q-parallel transport for Fenchel-Nielsen networks through q-nonabelianisation, and compare with quantum parallel transport computed using the Moore-Seiberg formalism. This motivates a proposal for a quantum version of the NRS proposal. In the second part, we reproduce Liouville conformal blocks through the standard free-field formalism with Fenchel-Nielsen-type integration contours. However, we observe that this approach is not complete with respect to wall-crossing. We therefore develop an extension of the free-field formalism to smooth spectral coverings, with the Maulik-Okounkov R-matrix playing a central role. We conjecture that this new formalism generates the full spectrum of Liouville conformal blocks, and provides a first-principle definition for Goncharov-Shen conformal blocks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25463 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Liouville Blocks from Spectral Networks Hollands, Lotte Murugesan, Subrabalan High Energy Physics - Theory Mathematical Physics Representation Theory In this paper, we investigate the role of spectral networks in quantum Liouville theory, with particular emphasis on spectral networks of Fenchel-Nielsen-type. In the first part, we construct q-parallel transport for Fenchel-Nielsen networks through q-nonabelianisation, and compare with quantum parallel transport computed using the Moore-Seiberg formalism. This motivates a proposal for a quantum version of the NRS proposal. In the second part, we reproduce Liouville conformal blocks through the standard free-field formalism with Fenchel-Nielsen-type integration contours. However, we observe that this approach is not complete with respect to wall-crossing. We therefore develop an extension of the free-field formalism to smooth spectral coverings, with the Maulik-Okounkov R-matrix playing a central role. We conjecture that this new formalism generates the full spectrum of Liouville conformal blocks, and provides a first-principle definition for Goncharov-Shen conformal blocks. |
| title | Liouville Blocks from Spectral Networks |
| topic | High Energy Physics - Theory Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2604.25463 |