Sampling using SU(N) gauge equivariant flows

@article{Boyda2020SamplingUS,
  title={Sampling using SU(N) gauge equivariant flows},
  author={Denis Boyda and Gurtej Kanwar and S{\'e}bastien Racani{\`e}re and Danilo Jimenez Rezende and M. S. Albergo and Kyle Cranmer and Daniel C. Hackett and Phiala Shanahan},
  journal={ArXiv},
  year={2020},
  volume={abs/2008.05456}
}
We develop a flow-based sampling algorithm for $SU(N)$ lattice gauge theories that is gauge-invariant by construction. Our key contribution is constructing a class of flows on an $SU(N)$ variable (or on a $U(N)$ variable by a simple alternative) that respect matrix conjugation symmetry. We apply this technique to sample distributions of single $SU(N)$ variables and to construct flow-based samplers for $SU(2)$ and $SU(3)$ lattice gauge theory in two dimensions. 
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