Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915817049817088 |
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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 |