2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217762We study the constraints of supersymmetry on the non-Abelian holonomy given by U=P exp(i\int A), the path-ordered exponential of a connection A. For theories with four supercharges, we show that A satisfies the tt* equations if it is a function of chiral multiplets. In contrast, when A is a function of vector multiplets, it satisfies the Bogomolnyi monopole equations. We describe applications of these results to the Berry connection in supersymmetric quantum mechanics.10 pages. v2 and v3: typos fixedHigh Energy Physics - TheoryQuantum Physicstext