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PreprintCC BY 4.0arXiv

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

  • Sarthak Duary
  • Sourav Maji
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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 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 C3=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 bs 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,bs sector.

Versions

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Cite

BibTeXRIS
BibTeX
@misc{duary2026path,
  title = {{Path integral quantization of null bosonic strings with Carroll-Weyl ghosts}},
  author = {Sarthak Duary and Sourav Maji},
  howpublished = {arXiv},
  year = {2026},
  month = jun,
  doi = {10.48550/arxiv.2606.04999},
  eprint = {2606.04999},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.04999},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Path integral quantization of null bosonic strings with Carroll-Weyl ghosts
AU  - Sarthak Duary
AU  - Sourav Maji
PY  - 2026
DA  - 2026/06/17
PB  - arXiv
DO  - 10.48550/arxiv.2606.04999
UR  - https://arxiv.org/abs/2606.04999
AB  - 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 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.
ER  -