Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere

Fuente: arXiv
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Autori principali: Zhou, Zheng, Gaiotto, Davide, He, Yin-Chen
Natura: Preprint
Pubblicazione: 2025
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author Zhou, Zheng
Gaiotto, Davide
He, Yin-Chen
author_facet Zhou, Zheng
Gaiotto, Davide
He, Yin-Chen
contents The fuzzy-sphere regularisation is a powerful tool to study conformal field theories (CFT) in three spacetime dimensions. In this paper, we extend its scope to CFTs with local fermionic operators. We realise the free-Majorana-fermion CFT on a set-up with one flavour of bosons and one flavour of fermions on the lowest Landau level with a $1/2$ angular momentum mismatch and allow conversion between two bosons and two fermions, and use a relative chemical potential as the tuning parameter. On the phase diagram, we observe two continuous transitions described respectively by a free Majorana fermion and a gauged Ising CFT. We numerically confirm the emergent conformal symmetry through the operator spectrum and the two-point correlation function of the local Majorana fermion. We further establish a correspondence between the fuzzy-sphere models and the field-theory Lagrangians, and extend it to an interacting fermionic CFT -- the super-Ising theory with emergent super-conformal symmetry.
format Preprint
id arxiv_https___arxiv_org_abs_2509_08038
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
Zhou, Zheng
Gaiotto, Davide
He, Yin-Chen
High Energy Physics - Theory
Mesoscale and Nanoscale Physics
Statistical Mechanics
Strongly Correlated Electrons
The fuzzy-sphere regularisation is a powerful tool to study conformal field theories (CFT) in three spacetime dimensions. In this paper, we extend its scope to CFTs with local fermionic operators. We realise the free-Majorana-fermion CFT on a set-up with one flavour of bosons and one flavour of fermions on the lowest Landau level with a $1/2$ angular momentum mismatch and allow conversion between two bosons and two fermions, and use a relative chemical potential as the tuning parameter. On the phase diagram, we observe two continuous transitions described respectively by a free Majorana fermion and a gauged Ising CFT. We numerically confirm the emergent conformal symmetry through the operator spectrum and the two-point correlation function of the local Majorana fermion. We further establish a correspondence between the fuzzy-sphere models and the field-theory Lagrangians, and extend it to an interacting fermionic CFT -- the super-Ising theory with emergent super-conformal symmetry.
title Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
topic High Energy Physics - Theory
Mesoscale and Nanoscale Physics
Statistical Mechanics
Strongly Correlated Electrons
url https://arxiv.org/abs/2509.08038