Defect Monstrous Moonshine



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19110040

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).