3d N=4 Bootstrap and Mirror Symmetry

Understand

We investigate the non-BPS realm of 3d ${\cal N} = 4$ superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d ${\cal N} = 4$ theories such as mirror symmetry and a protected sector described by topological quantum mechanics (TQM).

• Supersymmetric localization allows for the exact determination of the conformal and flavor central charges, and the latter can be fed into the mini-bootstrap of the TQM to solve for a subset of the OPE data.
• We examine the implications of the $\mathbb{Z}_2$ mirror action for the SCFT single- and mixed-branch crossing equations for the moment map operators, and apply numerical bootstrap to obtain universal constraints on OPE data for given flavor symmetry groups.
• A key ingredient in applying the bootstrap analysis is the determination of the mixed-branch superconformal blocks.