Fermionic Rational Conformal Field Theories and Modular Linear Differential Equations

Understand

We define Modular Linear Differential Equations (MLDE) for the level-two congruence subgroups $\Gamma_\vartheta$, $\Gamma^0(2)$ and $\Gamma_0(2)$ of $\text{SL}_2(\mathbb Z)$.

• Each subgroup corresponds to one of the spin structures on the torus.
• The pole structures of the fermionic MLDEs are investigated by exploiting the valence formula for the level-two congruence subgroups.
• We focus on the first and second order holomorphic MLDEs without poles and use them to find a large class of `Fermionic Rational Conformal Field Theories', which have non-negative integer coefficients in the $q$-series expansion of their characters.