= Two-form scalar duality
{title2=$H=g_B^2 *da$}
Locally in four dimensions, a massless two-form is dual to one real <scalar field>. In signature $(-+++)$, the first-order density $-H^2/(12g_B^2)+\epsilon^{\mu\nu\rho\sigma}H_{\mu\nu\rho}\partial_\sigma a/6$ gives $H^{\mu\nu\rho}=g_B^2\epsilon^{\mu\nu\rho\sigma}\partial_\sigma a$. Eliminating $H$ in both terms produces $-g_B^2(\partial a)^2/2$, so the fixed-normalization <kinetic coefficient> is inverted. Global flux sectors and scalar periodicities need separate treatment.
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