Worldsheets reconstructed: Duals to two-cut matrix models

@misc{pal2026worldsheets,
  title = {{Worldsheets reconstructed: Duals to two-cut matrix models}},
  author = {Sounak Pal},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08913},
  eprint = {2610.08913},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08913},
}

TY  - UNPB
TI  - Worldsheets reconstructed: Duals to two-cut matrix models
AU  - Sounak Pal
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08913
UR  - https://arxiv.org/abs/2610.08913
AB  - We compute the higher-rank translation (𝒯) and rotation (ℛ) matrices associated with a genus-one spectral curve. Using these data, we reconstruct the worldsheet correlators of vertex operators in the corresponding supersymmetric Landau--Ginzburg (LG) theory. This provides a generalization of the genus-zero, one-cut spectral-curve construction to higher-genus geometries. The matrix-model correlators are mapped to integrals over the moduli space of Riemann surfaces for the symmetric sextic double-well potential, which has a double-cut solution. We further identify the rational and elliptic contributions to the worldsheet integrated vertex operators and show that each of the sector precisely matches the corresponding correlators of single-trace operators in the matrix model. Altogether, our construction showcases an explicit dictionary between the higher-genus spectral-curve data, the associated Cohomological field theory (CohFT), and the worldsheet description of the corresponding matrix-model observables.
ER  -