Path integral quantization of null bosonic strings with Carroll-Weyl ghosts

Abstract

We revisit the path integral quantization of the null bosonic string from the viewpoint that all local gauge symmetries of the Carrollian worldsheet must be gauge fixed before the quantum theory is defined. In the tensile-string construction the $bc$ ghosts are the Faddeev-Popov determinant for fixing $\mathrm{Diff}\times\mathrm{Weyl}$. In the ILST null string this logic gives the BMS $bc$ system. However, a Carrollian worldsheet admits an additional volume-preserving Carroll-Weyl scaling, whose Hamiltonian generator is $C_3=P\cdot X$. Keeping this scaling as a genuine local gauge symmetry adds one more Faddeev-Popov row. The correct ghost system is therefore a $bcs$ system: the BMS $bc$ ghosts plus a scalar ghost $s$ and scalar antighost $b^s$ for Carroll-Weyl scaling. We derive the revised path integral, the $bcs$-ghost action, its residual symmetry equations, mode expansion, and its relation to the extended BMS algebra. The result changes the BRST complex and the anomaly problem: the usual $D=26$ check based only on the old BMS $bc$ ghosts is a partially gauge-fixed calculation, while the Carroll-Weyl covariant quantum theory must include the $s,b^s$ sector.