Duality defect of the monster CFT

Journal Article · Mon Jan 18 00:00:00 EST 2021 · Journal of Physics. A, Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8121/abd69e· OSTI ID:1851491

Lin, Ying-Hsuan ; Shao, Shu-Heng

Abstract We show that the fermionization of the Monster CFT with respect to ${\mathbb{Z}}_{2A}$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 ${\mathbb{Z}}_{2A}$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 thedefect McKay–Thompson seriesdefined 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 16D⁰of $PSL\left(2,\mathbb{Z}\right)$.

• Research Organization: California Institute of Technology (CalTech), Pasadena, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: SC0011632
• OSTI ID: 1851491
• Journal Information: Journal of Physics. A, Mathematical and Theoretical, Vol. 54, Issue 6; ISSN 1751-8113
• Publisher: IOP Publishing
• Country of Publication: United States
• Language: English

Related Subjects

Physics