= Supergravity coupling of an Abelian vector multiplet
{title2=$(A_\mu,\lambda)$}
An Abelian <vector multiplet> contains a <Maxwell field> and a Majorana <gaugino>. With the doubled <gravitino> normalization, add $e[-F^2/4-\bar\lambda\not\nabla\lambda/2-(\kappa/2)\bar\psi_\mu F_{ab}\gamma^{ab}\gamma^\mu\lambda]$. The leading transformations are $\delta A_\mu=\bar\epsilon\gamma_\mu\lambda$ and $\delta\lambda=-F_{ab}\gamma^{ab}\epsilon/2$. Promoting the rigid parameter to a function produces the current $(F_{ab}/2)\gamma^{ab}\gamma^\mu\lambda$ multiplying $\nabla_\mu\bar\epsilon$; the gravitino-current term cancels it. The Clifford identity $(F_{ab}\gamma^{ab})\gamma^\mu(F_{cd}\gamma^{cd})=8T_{\rm EM}^{\mu\nu}\gamma_\nu$ cancels the Maxwell stress variation. Supercovariant field strengths and quartic <fermions> complete the transformations beyond this order.
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