# Why is the string theory graviton spin-2?

In string theory, the first excited level of the bosonic string can be decomposed into irreducible representations of the transverse rotation group, $SO(D-2)$. We then claim that the symmetric traceless part (i.e. the 35 rep) is the spin-2 graviton - but isn't the label "spin-2" intrinsically 3+1 dimensional? I.e. it labels the representation under the little group $SU(2)$?

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