The "Zero Mode" in Kac Table: Revisiting the Ramond Sector of N=1 Superconformal Minimal Models

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We discover an infinite hierarchical web of the products of supersymmetric generators sustained by the superconformal Virasoro algebra. This hierarchy structure forms the mathematical foundation underpinning the explicit derivation of the character for the self-symmetric Ramond highest weight $c/24$. To consistently fit these exact results into the modular-invariant torus partition function, we advocate a necessary augmentation of the representation theory in the original Friedan--Qiu--Shenker construction via symmetrizing the ground-state manifold associated with the $c/24$ Verma module. Under the newly-proposed scheme, we invoke a quantum-interference mechanism between the two independent Ishibashi states to construct the boundary Cardy states for the whole family of the $\mathcal{N}=1$ superconformal minimal series, based on which the extra fusion channels are unveiled through the obtained Verlinde formula. Our work thus provides the first complete solution to this thirty-year-old question.