Anomaly mediation in Seiberg-Witten theories

We study the coupling of anomaly mediated supersymmetry breaking (AMSB) to $\mathcal{N}=2$ supersymmetric theories with $SU(2)$ gauge group. Perturbatively, $\mathcal{N}=1$ supersymmetry (SUSY) is preserved in the UV description with the AMSB terms being equivalent to a supersymmetric mass term for the adjoint chiral multiplet, as considered in the original Seiberg-Witten papers. We show, however, that nonperturbative instanton contributions break supersymmetry completely. In the IR description, the theory with AMSB is qualitatively similar to its $\mathcal{N}=1$ analog, exhibiting monopole condensation and confinement. However, the effective Lagrangian breaks supersymmetry completely, and the values of the condensates are different from their $\mathcal{N}=1$ analogs. Under physically reasonable assumptions, it can be shown that the vacua must change to those of the perturbatively identical $\mathcal{N}=1$-preserving deformation as the SUSY-breaking scale crosses the strong coupling scale. This change must be caused by effects that cannot in principle be described within the effective weakly coupled IR theory. It is not a phase transition, and the vacua appear to lie in the same universality class at any finite SUSY-breaking scale. Nonetheless, this work highlights the subtle manner in which AMSB coupling to nonperturbative effects can change the vacuum field configuration and the global symmetries of a theory.