Duality Defect of the Monster CFT

2019/10/31 by Ying-Hsuan Lin, Lin, Ying-Hsuan, Shu-Heng Shao +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Representation Theory (math.RT) #Strongly Correlated Electrons (cond-mat.str-el)

paper · pdf · doi:10.48550/arxiv.1911.00042

openalex publication_date 2019/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the fermionization of the Monster CFT with respect to ℤ_2A 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 ℤ_2A 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 16D⁰ of PSL(2,ℤ).

Citations

• Three-Dimensional Gravity Revisited

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