Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 306 / 4 / c

SetIts $L_0$ eigenvalue is $-1+2=1$. The Virasoro algebra givesso $L_1|s⟩=0$. At critical central charge $c=26$,so $L_2|s⟩=0$. All $L_n$ with $n\ge 3$ annihilate it directly. Hence $|s⟩$ is physical and, being a positive-level Virasoro descendant, spurious; it is therefore a null state.