Nonsupersymmetric Dualities from Mirror Symmetry

We study supersymmetry breaking perturbations of the simplest dual pair of ($2+1$)-dimensional $\mathcal{N}=2$ supersymmetric field theories—the free chiral multiplet and $\mathcal{N}=2$ super QED with a single flavor. We find dual descriptions of a phase diagram containing four distinct massive phases. The equivalence of the intervening critical theories gives rise to several nonsupersymmetric avatars of mirror symmetry: we find dualities relating scalar QED to a free fermion and Wilson-Fisher theories to both scalar and fermionic QED. Thus, mirror symmetry can be viewed as the multicritical parent duality from which these nonsupersymmetric dualities directly descend.

Figure 1

Phase diagram of theory $A$. Massless fields occur along the red lines (second order phase transitions).

Figure 2

Phase diagram of theory $B$.