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

Abstract

A bstract 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 Diff × 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 · 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 additional Carroll-Weyl gauge symmetry modifies both the BRST complex and the anomaly problem: the D = 26 condition arises in the two-constraint ILST analysis based on the BMS bc ghosts, whereas the Carroll-Weyl gauged theory contains the additional ( s , b s ) ghost sector and must be analyzed using the enlarged BRST complex.