= Field-strength force on a charged brane
{title2=$\delta\int_W X^*A=\int_W X^*(\iota_VF)+\int_{\partial W}X^*(\iota_VA)$}
For $F=dA$ and an embedding variation $V$, the pullback <Lie derivative> and <Cartan's magic formula> give the displayed variation. Consequently the interior force from the <Wess-Zumino brane coupling> depends only on the gauge-invariant field strength. A change $A\mapsto A+d\Lambda$ changes the action only on the boundary, by the <Generalized Stokes theorem>; boundaries require the appropriate fixed boundary data or additional boundary coupling.
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