= Bosonic ND boundary-changing conformal weight
{title2=$h_{\mathrm{ND}}=1/16$}
= ND twist conformal weight
{c}
{synonym}
For one free boson, the mixed ND open-string sector has strip vacuum energy $E_0=1/48$. The strip-to-plane transformation relates this energy to the plane <Virasoro algebra> zero mode by $E_0=h-c/24$, with <central charge> $c=1$. Hence its ground <conformal weight> is $h=1/48+1/24=1/16$. For $d$ independent ND coordinates the weights add to $d/16$. At $d=24$, the plane matter ground weight is $3/2$, while the strip oscillator vacuum energy is $1/2$. The plane physical condition $L_0^{\mathrm{plane}}-1=0$ is therefore equivalent to $\alpha'p_\parallel^2+N+1/2=0$. The apparent different constants are coordinate/constraint conventions, not different mass spectra.
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