I will describe the constraints due to modularity on the spectrum of two-dimensional SCFTs arising from compactification of M5 branes on divisors in one-parameter compact Calabi-Yau threefolds. These constraints are strong enough to determine the torus partition function (given by vector-valued modular forms for unit magnetic M5 charge) in terms of the polar terms. Consequently, our ansatz for the vector valued modular forms allows us to predict an infinite series of Donaldson-Thomas invariants associated with the target Calabi-Yau manifold. I will conclude with some comments on the exceptional cases of Calabi-Yau manifolds for which our ansatz fails, and on the cases with multiple M5 branes.

Based on work (2204.02207) in collaboration with Sergei Alexandrov, Jan Manschot, and Boris Pioline.