Simulating the non-unitary Yang-Lee conformal field theory on the fuzzy sphere
- 1University of California
- 2Harvard University
Abstract
A bstract The fuzzy sphere method has enjoyed great success in the study of (2+1)-dimensional unitary conformal field theories (CFTs) by regularizing them as quantum Hall transitions on the sphere. Here, we extend this approach to the Yang-Lee CFT — the simplest non-unitary CFT. We use an Ising quantum-Hall ferromagnet Hamiltonian with a transverse field and an imaginary longitudinal field, the latter breaks the Hermiticity of the Hamiltonian and thus the unitarity of the associated quantum field theory. Non-unitary conformal field theories — particularly the Yang-Lee CFT — pose significant challenges to conventional fuzzy sphere approaches. To overcome these obstacles, here we utilize a different method for determining critical points that requires no a priori knowledge of CFT scaling dimensions. Our method instead leverages the state-operator correspondence while utilizing two complementary criteria: the conformality of the energy spectrum and its consistency with conformal perturbation theory. We also discuss a new finite-size scaling on the fuzzy sphere that makes the sources of systematic error in extracting conformal data explicit, and compare it with the conventional analysis using the (1+1)-dimensional Yang-Lee problem as an example. Our results show broad agreement with previous Monte-Carlo and conformal bootstrap results. We also uncover one previously unknown primary operator and several operator product expansion coefficients.
Related
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BibTeX
@article{fan2026simulating,
title = {{Simulating the non-unitary Yang-Lee conformal field theory on the fuzzy sphere}},
author = {Ruihua Fan and Junkai Dong and Ashvin Vishwanath},
journal = {Journal of High Energy Physics},
year = {2026},
month = sep,
doi = {10.1007/jhep09(2026)041},
url = {https://doi.org/10.1007/jhep09(2026)041},
note = {CC BY},
}
RIS
TY - JOUR
TI - Simulating the non-unitary Yang-Lee conformal field theory on the fuzzy sphere
AU - Ruihua Fan
AU - Junkai Dong
AU - Ashvin Vishwanath
PY - 2026
DA - 2026/09/03
JO - Journal of High Energy Physics
DO - 10.1007/jhep09(2026)041
UR - https://doi.org/10.1007/jhep09(2026)041
AB - A bstract The fuzzy sphere method has enjoyed great success in the study of (2+1)-dimensional unitary conformal field theories (CFTs) by regularizing them as quantum Hall transitions on the sphere. Here, we extend this approach to the Yang-Lee CFT — the simplest non-unitary CFT. We use an Ising quantum-Hall ferromagnet Hamiltonian with a transverse field and an imaginary longitudinal field, the latter breaks the Hermiticity of the Hamiltonian and thus the unitarity of the associated quantum field theory. Non-unitary conformal field theories — particularly the Yang-Lee CFT — pose significant challenges to conventional fuzzy sphere approaches. To overcome these obstacles, here we utilize a different method for determining critical points that requires no a priori knowledge of CFT scaling dimensions. Our method instead leverages the state-operator correspondence while utilizing two complementary criteria: the conformality of the energy spectrum and its consistency with conformal perturbation theory. We also discuss a new finite-size scaling on the fuzzy sphere that makes the sources of systematic error in extracting conformal data explicit, and compare it with the conventional analysis using the (1+1)-dimensional Yang-Lee problem as an example. Our results show broad agreement with previous Monte-Carlo and conformal bootstrap results. We also uncover one previously unknown primary operator and several operator product expansion coefficients.
SN - 1029-8479
SN - 1126-6708
SN - 1127-2236
ER -