= Weyl-invariance exception for the string among branes
{c}
{title2=$p=1$}
Under $\gamma_{\mu\nu}\mapsto e^{2\omega}\gamma_{\mu\nu}$, the quadratic kinetic density of a $p$-brane scales as $e^{(p-1)\omega}$ and its constant density scales as $e^{(p+1)\omega}$. At $p=1$ the first factor is one and the constant term in the <auxiliary-metric brane action> vanishes. The traced metric equation is then an identity, leaving a <Weyl transformation> freedom. For $p\ne1$, the metric equation instead identifies the auxiliary and <induced worldvolume metrics>.
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