Duality Defect of the Monster CFT

Abstract

We show that the fermionization of the Monster CFT with respect to ${\mathbb{Z}}_{2A}$ 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 ${\mathbb{Z}}_{2A}$ 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 $16D^0$ of $PSL(2,\mathbb{Z})$.

26+9 pages, 7 figure, 4 tables. v2: minor changes

References in corpus (6)

• Generalized Global Symmetries
• Three-Dimensional Gravity Revisited
• Duality and defects in rational conformal field theory
• Topological Transition on the Conformal Manifold
• Anomalies and Bounds on Charged Operators
• Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions

Cited by in corpus (5)

• Lorentzian Dynamics and Factorization Beyond Rationality
• Conformal Field Theories with Sporadic Group Symmetry
• Bootstrapping Fermionic Rational CFTs with Three Characters
• Fermionic Rational Conformal Field Theories and Modular Linear Differential Equations
• von Neumann Subfactors and Non-invertible Symmetries