Free-end string boundary condition (source code)

= Free-end string boundary condition
{title2=$X'^m|_{\partial\Sigma}=0$}

Free endpoint variations set the <open string> flux $eT^2X'_m+uP_m$ to zero. In a boundary-adapted temporal gauge, freedom to vary time forces $u=0$ at the end. Nonzero lapse then gives $X'^m=0$, a <Neumann boundary condition>.