Two-dimensional RCFT’s without Kac-Moody symmetry
Harsha Hampapura (Indian Institute of Science Education and Research, Homi Bhabha Rd, Pashan, Pune, 411 008, India); Sunil Mukhi (Yukawa Institute of Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan, Indian Institute of Science Education and Research, Homi Bhabha Rd, Pashan, Pune, 411 008, India)
Using the method of modular-invariant differential equations, we classify a family of Rational Conformal Field Theories with two and three characters having no Kac-Moody algebra. In addition to unitary and non-unitary minimal models, we find “dual” theories whose characters obey bilinear relations with those of the minimal models to give the Moonshine Module. In some ways this relation is analogous to cosets of meromorphic CFT’s. The theory dual in this sense to the Ising model has central charge 47 2 $$ \frac{47}{2} $$ and is related to the Baby Monster Module.
