Particle Theory Seminar - Naveen Umasankar - “Do novel Rational Conformal Field Theories lurk in extensions of modular subgroups?”

The space of Rational Conformal Field Theories (RCFTs) is understood by observing their classification. One classification scheme based on the modular group, SL(2, Z), is the Mathur-Mukhi-Sen approach done in the 80s. In this talk, I will set up and discuss admissible solutions to modular linear differential equations of various extensions of subgroups of SL(2, Z) called Fricke groups, and their use in the classification of RCFTs. I will also discuss surprising connections to number theory and approaches to realizing the admissible solutions in terms of known CFTs.