= Gauge invariance of an open-brane coupling
{title2=$S=q\int_WX^*C+q\int_{\partial W}X^*B$}
For an oriented <brane> worldvolume $W$, a <gauge transformation> $C\mapsto C+d\Lambda$ changes the <Wess-Zumino brane coupling> by $q\int_{\partial W}X^*\Lambda$, by the <Generalized Stokes theorem>. If the brane boundary lies on a manifold carrying a form $B$ of one lower degree, adding the displayed boundary term and transforming $B\mapsto B-\Lambda$ cancels this variation. The sign uses the induced boundary orientation. A closed worldvolume needs no boundary term; noncompact cases require appropriate support or decay conditions.
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