Gauge-invariant string coupling to a two-form
= Gauge-invariant string coupling to a two-form
{title2=$q\int_\Sigma X^*B$}
The coupling $q\int_\Sigma X^*B$ integrates the pullback of the <two-form gauge field> over the <string worldsheet>. Its gauge variation is $q\int_{\partial\Sigma}X^*\alpha$, by <Stokes theorem>. It therefore vanishes for a closed worldsheet, while an open surface requires suitable boundary fields or boundary-state transformations.