Description
We discuss a sufficient (but not necessary) condition for partition functions of QFTs to vanish, meaning that generic correlators are zero unless suitable operators are inserted. Vanishing partition functions have been observed in multiple occasions in the past. Here we provide a systematic perspective from the moduli space to unify these seemingly independent results. In the context of D-branes, we recover the Freed-Witten anomaly cancellation condition, and our approach allows us to extend it to branes in non-perturbative string/M-theory backgrounds.