Relations between supersymmetric structures in UV and IR for $\mathcal{N}=4$ bad theories

Abstract

We investigate options for the structure of the infrared fixed points of $\mathcal{N}=4$ bad theories in three dimensions. Unitarity constraints allow a number of possibilities, not necessarily a product of an interacting $\mathcal{N}=4$ SCFT and free theories. For each option we provide relations between the UV and IR $R-$symmetry groups. For some of them we give examples. In particular, the $\mathcal{N}4$ SU(2) SYM with two fundamental hypermultiplets is an example of a bad theory which flows to an interacting irreducible SCFT in the IR. The question of whether all the options are realized remains open.

26 pages, v2: discussion of SU(2) SYM with two fundamental hypers added, references added, some minor corrections, v3: typos corrected, minor changes, version published in JHEP

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• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Supersymmetry enhancement by monopole operators
• On Three Dimensional Quiver Gauge Theories and Integrability
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Cited by in corpus (9)

• Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
• The Infrared Physics of Bad Theories
• The $SL(2,\mathbb{Z})$ dualization algorithm at work
• Good IR Duals of Bad Quiver Theories
• Index and duality of minimal N=4 Chern-Simons-matter theories
• Resolved gravity duals of $\mathcal{N}=4$ quiver field theories in 2+1 dimensions
• Holographic Duality for three-dimensional Super-conformal Field Theories
• Non-Perturbative Schwinger-Dyson Equations for 3d $\mathcal{N}=4$ Gauge Theories
• Factorization of the 3d superconformal index with an adjoint matter