virasoro_blocks: Software for the 2d bootstrap
Abstract
We introduce virasoro_blocks, software that computes Virasoro conformal blocks at any central charge in a form suitable for the numerical bootstrap. At each finite order in the elliptic nome, Zamolodchikov's recursion gives the block as a positive prefactor times a rational function of the exchanged weight. However, its many Kac poles make it difficult to use in semidefinite programming approaches to the bootstrap. In this software we use optimal interpolation to reduce the number of poles while keeping high accuracy. The software works in arbitrary precision and handles singular central charges, including the minimal models and c=1. It also computes global blocks, N=1 superconformal blocks, torus characters, and torus one-point blocks. We illustrate it with two applications. Assuming only scalar Virasoro primaries, we compute bounds on the scalar gap that approach the window of Liouville solutions between (c−1)/16 and (c−1)/12. We also bound the average exchanged dimension in four-point functions of identical scalars at several central charges. These bounds have a rich structure, and many known 2d CFTs lie on or near their boundary.
Related
- Virasoro Conformal Blocks and modular functor from Liouville CFT
- The Virasoro Bootstrap: from the c∼1 desert to coupled Potts
- A Dispersive Bootstrap for the Virasoro-Shapiro Amplitude
- Conformal blocks and braiding matrices for RCFTs I: Virasoro minimal models
- Super Liouville theory on the torus: bootstrap and the super Virasoro minimal string
BibTeX
@misc{poland2026virasoroblocks,
title = {{virasoro_blocks: Software for the 2d bootstrap}},
author = {David Poland},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39106},
eprint = {2610.39106},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39106},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - virasoro_blocks: Software for the 2d bootstrap
AU - David Poland
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39106
UR - https://arxiv.org/abs/2610.39106
AB - We introduce virasoro_blocks, software that computes Virasoro conformal blocks at any central charge in a form suitable for the numerical bootstrap. At each finite order in the elliptic nome, Zamolodchikov's recursion gives the block as a positive prefactor times a rational function of the exchanged weight. However, its many Kac poles make it difficult to use in semidefinite programming approaches to the bootstrap. In this software we use optimal interpolation to reduce the number of poles while keeping high accuracy. The software works in arbitrary precision and handles singular central charges, including the minimal models and c=1. It also computes global blocks, N=1 superconformal blocks, torus characters, and torus one-point blocks. We illustrate it with two applications. Assuming only scalar Virasoro primaries, we compute bounds on the scalar gap that approach the window of Liouville solutions between (c−1)/16 and (c−1)/12. We also bound the average exchanged dimension in four-point functions of identical scalars at several central charges. These bounds have a rich structure, and many known 2d CFTs lie on or near their boundary.
ER -