Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 306 / 2 / 3 / Solution

Adding the matter and ghost transformations givesFor the Laurent modes $L_n=\oint dz{z}^{n+1}{T}_{\mathrm{tot}}(z)/(2\pi i)$, the corresponding Virasoro algebra isAt the bosonic-string critical dimension of string theory, $D=26$, the total central charge and central term vanish. The total stress tensor then transforms as a genuine conformal tensor of weight two, and the quantum worldsheet gauge anomaly cancels.