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In a nutshell, the $1+1=2$ extra dimensions of spacetime can (in an appropriate gauge) be viewed as a longitudinal spatial direction and a temporal direction. This makes sense because of Minkowski signature of spacetime. The point is that the physical modes of the string can be identified with the 24 (8) transversal directions of the critical bosonic ...


The two notions are indeed related. Take for example the Weyl anomaly of bosonic string theory: the classical (Polyakov) action $S$ is invariant under Weyl rescalings of the worldsheet metric $\gamma_{ab}$, i.e. $$S[\gamma_{ab}(\tau,\sigma)]=S[\exp(2\omega(\tau,\sigma))\gamma_{ab}(\tau,\sigma)]=S[\gamma'_{ab}(\tau,\sigma)].$$ Since this is a conformal ...

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