Charged-multiplet formula for elliptic Calabi–Yau threefolds

Let $X \to B$ be an equidimensional elliptic Calabi-Yau threefold with $\mathbb{Q}$-factorial terminal singularities and reduced discriminant $\Sigma$, whose divisorial components are $\Sigma_j$. Assume that $\Sigma_m \not\subset \Sigma_j$ for every $j$. For a representation $\rho$ of a Lie algebra with Cartan subalgebra, let $(\dim \rho)_{ch}$ denote its charged dimension, and let $g(\Sigma_j)$, $g_j'$, $g_j$, $\rho_{0,j}$, $\rho_Q$, and $c_Q$ be the quantities defined in the source.

Charged-multiplet conjecture. The charged multiplets $H_{ch}$ in the massless spectrum satisfy

$$H_{ch}=\sum_j g(\Sigma_j)(\dim \operatorname{adj}_j)_{ch}+\sum_j(g_j'-g_j)(\dim \rho_{0,j})_{ch}+\sum_Q(\dim \rho_Q)_{ch}+\sum_Q c_Q.$$

This formula is intended to describe the charged part of the massless spectrum of elliptically fibered Calabi–Yau threefolds in terms of geometric and representation-theoretic data. The supplied text does not state whether the conjecture has been proved or disproved.