Anomalies, tori, and new twists in the gaugino condensate

I will first review some recent advances in the understanding of generalized-symmetry anomalies in four dimensional gauge theories and will show that they imply  degeneracies in the Hilbert space on appropriately twisted tori. Quite unusually, these degeneracies are exact for any size tori. I will then explain how this understanding helps improve and interpret the semiclassical calculation of the gaugino condensate in super-Yang-Mills theory in the framework of the twisted femtouniverse, first attempted in 1984. I will discuss the salient points and present some outstanding puzzles, to provoke discussion and stimulate further thoughts about semiclassics and continuity.