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Recent advances in condensed matter physics have shown that the spin degree of freedom of electrons can be efficiently exploited in the emergent field of spintronics, offering unique opportunities for efficient data transfer, computing, and storage (1–3). These concepts have been inspiring analogous approaches in photonics, where the manipulation of an artificially engineered pseudospin degree of freedom can be enabled by synthetic gauge fields acting on light (4–6). The ability to control these degrees of freedom significantly expands the landscape of available optical responses, which may revolutionize optical computing and the basic means of controlling light in photonic devices across the entire electromagnetic spectrum. We demonstrate a new class of photonic systems, described by effective Hamiltonians in which competing synthetic gauge fields, engineered in pseudospin, chirality/sublattice, and valley …