On Supersymmetric Lifshitz Field Theories

TL;DR

This paper explores supersymmetric Lifshitz field theories, constructing their algebra, analyzing interactions, and revealing how quantum effects influence scale invariance across different dimensions.

Contribution

It introduces a supersymmetric Lifshitz field theory framework with a novel algebra and examines quantum interactions and symmetry breaking in various dimensions.

Findings

Constructed free field supersymmetry algebra for even z

Identified supersymmetry-preserving quantum cancellations

Found Lifshitz scale invariance broken in 3+1 dimensions

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.