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arXiv · 2609.00148

Regulating Free-scalar and Yang--Lee 5d CFTs on the Fuzzy Four Sphere

Jiangyuan Qian
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Abstract

Non-commutative sphere regularization of CFT has become a powerful tool for computing conformal data of 3d CFTs and was recently extended to 4d CFTs. In this work we further construct 5d free-scalar CFT and Yang-Lee CFT on a fuzzy 4-sphere. We observe a continuous phase transition and conformal towers in these examples. We obtain the first three scalar primaries of the 5d free-scalar CFT, furthermore, we compute the 5d Yang-Lee $\Delta_\phi,\Delta_{\phi^3}$ with $N_e=10$ fermions using exact diagonalization (ED) and $N_e=20$ fermions using density matrix renormalization group (DMRG), obtaining relatively good agreement with both $\epsilon$-expansion and the Gliozzi truncated bootstrap result.

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Jiangyuan Qian. 2026-08-31. Regulating Free-scalar and Yang--Lee 5d CFTs on the Fuzzy Four Sphere. https://arxiv.org/abs/2609.00148

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