Reconstruction of the conformal algebra from a critical groundstate on the (fuzzy) sphere
Abstract
Recently, we found a method to reconstruct the dilatation operator (sphere Hamiltonian) from a regulated conformal field theory groundstate. In this paper, we explore methods to construct the whole global conformal algebra, and test our construction using fuzzy sphere regularization. Starting from a groundstate of the same Hamiltonian, these methods perform better than constructions of the conformal generators based on a Hamiltonian density, are model-independent, require no additional tuning, and improve with system size. One purpose of reconstructing the conformal algebra is to identify conformal primary states, which we do with some success. We also find further evidence supporting the model of the short-distance corrections to the entanglement Hamiltonian proposed earlier and use it to make systematic improvements.
Related
- Certified reduced-basis emulation of conformal field theories on the fuzzy sphere
- Conformal boundaries and the photon sphere of AdS black holes
- The Conformal w-Algebra
- Conformal data for the O(2) Wilson-Fisher CFT in (2+1)-dimensional spacetime from exact diagonalization and matrix product states on the fuzzy sphere
- Simulating the non-unitary Yang-Lee conformal field theory on the fuzzy sphere
BibTeX
@misc{camasca2026reconstruction,
title = {{Reconstruction of the conformal algebra from a critical groundstate on the (fuzzy) sphere}},
author = {Rolando Ramirez Camasca and Xiang Li and Ting-Chun Lin and John McGreevy},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03817},
eprint = {2611.03817},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03817},
}
RIS
TY - UNPB
TI - Reconstruction of the conformal algebra from a critical groundstate on the (fuzzy) sphere
AU - Rolando Ramirez Camasca
AU - Xiang Li
AU - Ting-Chun Lin
AU - John McGreevy
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03817
UR - https://arxiv.org/abs/2611.03817
AB - Recently, we found a method to reconstruct the dilatation operator (sphere Hamiltonian) from a regulated conformal field theory groundstate. In this paper, we explore methods to construct the whole global conformal algebra, and test our construction using fuzzy sphere regularization. Starting from a groundstate of the same Hamiltonian, these methods perform better than constructions of the conformal generators based on a Hamiltonian density, are model-independent, require no additional tuning, and improve with system size. One purpose of reconstructing the conformal algebra is to identify conformal primary states, which we do with some success. We also find further evidence supporting the model of the short-distance corrections to the entanglement Hamiltonian proposed earlier and use it to make systematic improvements.
ER -