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Physlib.QFT.QED.AnomalyCancellation.LowDim.Two

1 declaration

definition

Equivalence between linear and cubic solutions for n=2n=2 pure U(1)U(1) theory

#equiv

For a pure U(1)U(1) gauge theory with n=2n=2 fermions, this is the equivalence between the space of linear solutions and the space of full solutions. Specifically, it maps a solution of the linear gravitational anomaly condition, x1+x2=0x_1 + x_2 = 0, to a solution of the full system of Anomaly Cancellation Conditions (ACCs), which includes both the linear condition and the cubic gauge anomaly condition x13+x23=0x_1^3 + x_2^3 = 0. This equivalence is based on the mathematical fact that for any x1,x2Qx_1, x_2 \in \mathbb{Q}, the linear constraint x1+x2=0x_1 + x_2 = 0 implies the cubic constraint x13+x23=0x_1^3 + x_2^3 = 0.