In 2D Euclidean space, QED with fermions can be written as a first-order gravity theory with a parity-violating fermion coupling, but the claimed quantum equivalence is not fully established.
Exact solutions of classical electrody namics and the Yang-Mills-Wong theory in even-dimensional space-time
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Relating electrodynamics and gravity in two Euclidean dimensions
In 2D Euclidean space, QED with fermions can be written as a first-order gravity theory with a parity-violating fermion coupling, but the claimed quantum equivalence is not fully established.