The U ( 1 ) piece can be identified with electromagnetism in several different ways. One way is that the Dirac operators on the spin manifold, when squared, contain a piece F = d A with A arising from that part of the connection associated with the U ( 1 ) piece. This is entirely analogous to what happens when one squares the ordinary Dirac equation in ordinary Minkowski spacetime. A second hint is that this U ( 1 ) piece is associated with the determinant bundle of the spin structure, effectively tying together the left and right-handed spinors through complex conjugation.