Spinor Pairs and the Concentration Principle for Dirac operators

We study perturbed Dirac operators of the form $ D_s= D + s{\cal A} :\Gamma(E)\rightarrow \Gamma(F)$overacompactRiemannianmanifold$(X, g)$withsymbol$c$andspecialbundlemaps${\cal A} : E\rightarrow F$for$s>>0$. Under a simple algebraic criterion on the pair $(c,\mathcal{A})$, solutions of $D_s\psi =0$ concentrate as $s\to \mathrm{\infty }$ around the singular set $Z_{\text{A}}\subset X$ of $\mathcal{A}$. We give many examples, the most interesting ones arising from a general ``spinor pair’’ construction.