= Superspace Yang-Mills Bianchi identity
{title2=$D^\alpha W_\alpha=\bar D_{\dot\alpha}\bar W^{\dot\alpha}$}
For a real Abelian <vector superfield>, $W_\alpha=-\bar D^2D_\alpha V/4$ is chiral. The <supercovariant derivative algebra with left derivatives> gives $D^\alpha\bar D^2D_\alpha=\bar D_{\dot\alpha}D^2\bar D^{\dot\alpha}$, proving the displayed reality condition. Its component equations contain the ordinary <gauge-theory Bianchi identity>, not the <Maxwell equations> of motion. For a non-Abelian <gauge group>, replace these by gauge-covariant derivatives and compare both field strengths in the same gauge frame; the identity follows from the <graded Jacobi identity> of the superconnection.
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