  Circuits can provide a platform to study novel physics and have been used,
for example, to explore various topological phases. Gauge fields-particularly,
non-Abelian gauge fields-can play a pivotal role in the design and modulation
of novel physical states, but their circuit implementation has so far been
limited. Here we show that non-Abelian gauge fields can be synthesized in
circuits created from building blocks that consist of capacitors, inductors and
resistors. With these building blocks, we create circuit designs for the
spin-orbit interaction and the topological Chern state, which are phenomena
that represent non-Abelian gauge fields in momentum space. We also use the
approach to design non-reciprocal circuits that can be used to implement the
non-Abelian Aharonov-Bohm effect in real space.
