Defect Monstrous Moonshine


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


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


          @misc{ pirsa_19110040,
            doi = {},
            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}}


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).