On Supersymmetric Lifshitz Field Theories

Abstract

We consider field theories that exhibit a supersymmetric Lifshitz scaling with two real supercharges. The theories can be formulated in the language of stochastic quantization. We construct the free field supersymmetry algebra with rotation singlet fermions for an even dynamical exponent $z=2k$ in an arbitrary dimension. We analyze the classical and quantum $z=2$ supersymmetric interactions in $2+1$ and $3+1$ spacetime dimensions and reveal a supersymmetry preserving quantum diagrammatic cancellation. Stochastic quantization indicates that Lifshitz scale invariance is broken in the $(3+1)$-dimensional quantum theory.

26 pages

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• The anisotropic chiral boson
• Non-Relativistic Supersymmetry on Curved Three-Manifolds
• Supersymmetric Soliton $\sigma$-models from Non-Lorentzian Field Theories
• Non-Local Deformation of a Supersymmetric Field Theory
• RG Flows and Symmetry Enhancement in Five-Dimensional Lifshitz Gauge Theories
• Generalised Bargmann Superalgebras
• Developments in non-relativistic field theory and complexity