Conformal scalar field theory from Ising tricriticality on the fuzzy sphere
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916814357790720 |
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| author | Taylor, Joseph Voinea, Cristian Papić, Zlatko Fan, Ruihua |
| author_facet | Taylor, Joseph Voinea, Cristian Papić, Zlatko Fan, Ruihua |
| contents | Free theories are landmarks in the landscape of quantum field theories: their exact solvability serves as a pillar for perturbative constructions of interacting theories. Fuzzy sphere regularization, which combines quantum Hall physics with state-operator correspondence, has recently been proposed as a promising framework for simulating three-dimensional conformal field theories (CFTs), but so far it has not provided access to free theories. We overcome this limitation by designing a bilayer quantum Hall system that hosts an Ising tricritical point -- a nontrivial fixed point where first-order and second-order transitions meet -- which flows to the conformally coupled scalar theory in the infrared. The critical energy spectrum and operator structure match those at the Gaussian fixed point, providing nonperturbative evidence for the emergence of a free scalar CFT. Our results expand the landscape of CFTs realizable on the fuzzy sphere and demonstrate that even free bosonic theories -- previously inaccessible -- can emerge from interacting electrons in this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22539 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformal scalar field theory from Ising tricriticality on the fuzzy sphere Taylor, Joseph Voinea, Cristian Papić, Zlatko Fan, Ruihua Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Free theories are landmarks in the landscape of quantum field theories: their exact solvability serves as a pillar for perturbative constructions of interacting theories. Fuzzy sphere regularization, which combines quantum Hall physics with state-operator correspondence, has recently been proposed as a promising framework for simulating three-dimensional conformal field theories (CFTs), but so far it has not provided access to free theories. We overcome this limitation by designing a bilayer quantum Hall system that hosts an Ising tricritical point -- a nontrivial fixed point where first-order and second-order transitions meet -- which flows to the conformally coupled scalar theory in the infrared. The critical energy spectrum and operator structure match those at the Gaussian fixed point, providing nonperturbative evidence for the emergence of a free scalar CFT. Our results expand the landscape of CFTs realizable on the fuzzy sphere and demonstrate that even free bosonic theories -- previously inaccessible -- can emerge from interacting electrons in this framework. |
| title | Conformal scalar field theory from Ising tricriticality on the fuzzy sphere |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.22539 |