Do vertex algebra characters obey modular symmetry?

When you wrap a vertex algebra around an elliptic curve and ask which character formulas stay invariant under transformations, the answer involves a special property called holonomicity. The team proves this works for large classes of algebras arising in physics—affine algebras and W-algebras—by showing that conformal blocks satisfy a rigid differential equation. The result confirms a longstanding conjecture and generalizes Zhu's foundational theorem from 1996.