  Non-Abelian gauge fields provide a conceptual framework for the description
of particles having spins. The theoretical importance of non-Abelian gauge
fields motivates their experimental synthesis and explorations. Here, we
demonstrate non-Abelian lattice gauge fields for photons. In the study of gauge
fields, lattice models are essential for the understanding of their
implications in extended systems. We utilize the platform of synthetic
frequency dimensions, which enables the study of lattice physics in a scalable
and programmable way. We observe Dirac cones at time-reversal-invariant momenta
as well as the direction reversal of eigenstate trajectories associated with
such Dirac cones. Both of them are unique signatures of non-Abelian gauge
fields in our lattice system. Our results highlight the implications of
non-Abelian gauge field in the study of topological physics and suggest
opportunities for the control of photon spins and pseudospins.
