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Given a swarm of limited-capability robots, we seek to automatically discover the set of possible emergent behaviors. Prior approaches to behavior discovery rely on human feedback or hand-crafted behavior metrics to represent and evolve behaviors and only discover behaviors in simulation, without testing or considering the deployment of these new behaviors on real robot swarms. In this work, we present Real2Sim2Real Behavior Discovery via Self-Supervised Representation Learning, which combines representation learning and novelty search to discover possible emergent behaviors automatically in simulation and enable direct controller transfer to real robots. First, we evaluate our method in simulation and show that our proposed self-supervised representation learning approach outperforms previous hand-crafted metrics by more accurately representing the space of possible emergent behaviors. Then, we address the reality gap by incorporating recent work in sim2real transfer for swarms into our lightweight simulator design, enabling direct robot deployment of all behaviors discovered in simulation on an open-source and low-cost robot platform.