# Defect Monstrous Moonshine

### APA

Shao, S. (2019). Defect Monstrous Moonshine. Perimeter Institute. https://pirsa.org/19110040

### MLA

Shao, Shu-Heng. Defect Monstrous Moonshine. Perimeter Institute, Nov. 26, 2019, https://pirsa.org/19110040

### BibTex

@misc{ pirsa_PIRSA:19110040, doi = {10.48660/19110040}, url = {https://pirsa.org/19110040}, author = {Shao, Shu-Heng}, keywords = {Quantum Fields and Strings}, language = {en}, title = {Defect Monstrous Moonshine}, publisher = {Perimeter Institute}, year = {2019}, month = {nov}, note = {PIRSA:19110040 see, \url{https://pirsa.org}} }

Shu-Heng Shao Stony Brook University

**Collection**

**Talk Type**Scientific Series

**Subject**

## Abstract

The Monster CFT is a (1+1)d holomorphic CFT with the Monster group global symmetry. The symmetry twisted partition functions exhibit the celebrated Monstrous Moonshine Phenomenon. From a modern point of view, topological defects generalize the notion of global symmetries. We argue that the Monster CFT has a Kramers-Wannier duality defect that is not associated with any global symmetry. The duality defect extends the Monster group to a larger category of topological defects 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 it is invariant under the genus-zero congruence subgroup 16D0 of PSL(2,Z).