Nonlinear sigma models, antiperiodic boundary conditions, spin chains, and 't Hooft anomalies (opens in new tab)

We consider two sets of related models: initially, these are $SU(2)$ antiferromagnetic spin chains with $N$ sites of spin $S$, and the $O(3)$ nonlinear sigma model in two dimensions with topological coefficient $\Theta$ a multiple of $\pi$ (and later, the extensions of these with any semisimple Lie group symmetry). It is known that, in a continuum description, the low-energy behavior of the spin chain is given by the sigma model with $\Theta=2\p...