2026/05/11 by Yamato Honda, Justin Kaidi, Ippo Orii · 1 voice
#hep-th #cond-mat.str-el #math.QA #math.RT
We study the parafermionization of the Monster CFT with respect to its ℤpA subgroups, with p an odd prime. Under certain assumptions, we show that the parafermionization is equal to a non-invertible gauging of P(p) × P(p)^\vee, where P(p) is the theory of ℤp-parafermions and P(p)^\vee is an appropriate dual theory, with global symmetry characterized by the centralizer of ℤpA. By tracking the symmetries of P(p) × P(p)^\vee through the non-invertible gauging, we argue that the diagonal Monster CFT has Rep(\mathfrakso(3)p) \boxtimes Rep(\mathfrakso(3)p)op symmetry, and hence that the holomorphic Monster theory has symmetry Rep(\mathfrakso(3)p). We then compute the defect McKay-Thompson series associated to these symmetries, and prove that their invariance subgroups are Γ1(p+2).