Rectifiability and Minkowski bounds for the zero loci of Z/2 harmonic spinors

Abstract: We prove that the zero locus of a Z/2 harmonic spinor on a 4-manifold is 2-rectifiable and has finite Minkowski content. This result improves a regularity result by Taubes in 2014. It gives more precise descriptions to the limit behaviors of non-convergent sequences of solutions to many gauge-theoretic equations, such as Kapustin-Witten equations, Vafa-Witten equations, and Seiberg-Witten equations with multiple spinors.