Abstract
Lagrangian gauge theories with a z = 2 Lifshitz scaling provide a family of interacting, asymptotically free five-dimensional field theories. We examine a broad class of these theories, including some of their quantum properties, extending previous results to include matter. We present no-go theorems that, in the absence of constraints, the class of theories we consider cannot admit a spinorial supersymmetry or Galilean boost symmetry. However, we argue that there exist renormalization group flows whose fixed points can admit supersymmetry and boosts, i.e. super-Schrödinger symmetry. We also present examples of Lifshitz gauge theories with a scalar supersymmetry.
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