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

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 ${\Delta }_{\varphi },{\Delta }_{{\varphi }^3}$ 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.

19 pages, 8 figures