Lin, Ying-Hsuan and Shao, Shu-Heng (2021) Duality defect of the monster CFT. Journal of Physics A: Mathematical and Theoretical, 54 (6). Art. No. 065201. ISSN 1751-8113. doi:10.1088/1751-8121/abd69e. https://resolver.caltech.edu/CaltechAUTHORS:20191106-101344650
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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).
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| Additional Information: | © 2021 IOP Publishing Ltd. Received 25 October 2020; Revised 20 December 2020; Accepted 24 December 2020; Published 18 January 2021. We thank Nathan Benjamin, Meng Cheng, Wenjie Ji, Petr Kravchuk, Theo Johnson-Freyd, Natalie Paquette, and Xiao-Gang Wen for discussions. SHS would like to thank Kantaro Ohmori and Nathan Seiberg for useful discussions on global symmetries in bosonic and fermionic QFTs. We thank Theo Johnson-Freyd for comments on the draft. YL is supported by the Sherman Fairchild Foundation, and by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. The work of SHS is supported by the Simons Foundation/SFARI (651444, NS). | |||||||||
| Group: | Walter Burke Institute for Theoretical Physics | |||||||||
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| Subject Keywords: | Monster,Baby Monster, topological defect,Kramers–Wannier duality, McKay–Thompson, fermionization, moonshine | |||||||||
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| Issue or Number: | 6 | |||||||||
| DOI: | 10.1088/1751-8121/abd69e | |||||||||
| Record Number: | CaltechAUTHORS:20191106-101344650 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20191106-101344650 | |||||||||
| Official Citation: | Ying-Hsuan Lin and Shu-Heng Shao 2021 J. Phys. A: Math. Theor. 54 065201 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 99690 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Joy Painter | |||||||||
| Deposited On: | 06 Nov 2019 18:28 | |||||||||
| Last Modified: | 12 Jul 2022 19:50 |
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