Non-Abelian Berry Phase, Instantons and N=(0,4) Supersymmetry

Understand

In supersymmetric quantum mechanics, the non-Abelian Berry phase is known to obey certain differential equations.

• Here we study N=(0,4) systems and show that the non-Abelian Berry connection over R^{4n} satisfies a generalization of the self-dual Yang-Mills equations.
• Upon dimensional reduction, these become the tt* equations.
• We further study the Berry connection in N=(4,4) theories and show that the curvature is covariantly constant.