We show that the fermionization of the Monster CFT with respect to is the tensor product of a free fermion and the Baby Monster CFT. The chiral fermion parity of the free fermion implies that the Monster CFT is self-dual under the orbifold, i.e. it enjoys the Kramers–Wannier duality. The Kramers–Wannier duality defect extends the Monster group to a larger category of topological defect lines that contains an Ising subcategory. We introduce the defect McKay–Thompson series defined as the Monster partition function twisted by the duality defect, and find that the coefficients can be decomposed into the dimensions of the (projective) irreducible representations of the Baby Monster group. We further prove that the defect McKay–Thompson series is invariant under the genus-zero congruence subgroup 16D ⁰ of .

我们表明，相对于怪物CFT的fermionization是自由费密子和Baby Monster CFT的张量积。游离费米子的手性费米子平价意味着Monster CFT在球型之下是自对偶的，即它具有Kramers-Wannier对偶性。Kramers-Wannier对偶缺陷将Monster组扩展到包含Ising子类别的较大类别的拓扑缺陷线。我们介绍缺陷麦凯-汤普森系列定义为被对偶缺陷扭曲的Monster分区函数，发现该系数可以分解为Baby Monster组的（投影）不可约表示的维数。我们进一步证明了缺陷McKay-Thompson级数在的属零同余子集16 D ⁰下是不变的。