3d N=4 Bootstrap and Mirror Symmetry

Abstract

We investigate the non-BPS realm of 3d $\mathcal{N}=4$ superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d $\mathcal{N}=4$ 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. Among other results, we show that the simplest known self-mirror theory with $SU(2)\times SU(2)$ flavor symmetry saturates our bootstrap bounds, which allows us to extract the non-BPS data and examine the self-mirror ${\mathbb{Z}}_2$ symmetry thereof.

50+27 pages, 6 figures, 7 tables. v2: typos corrected, references added. v3: a brief summary added, minor notations changed, SciPost published version

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Cited by in corpus (7)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• The topological line of ABJ(M) theory
• Bootstrapping (D, D) Conformal Matter
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
• Fermi-gas correlators of ADHM theory and triality symmetry