BRST quantization of Carroll-Weyl gauged null strings
Abstract
We study the BRST quantization of the null string after completing its local gauge symmetry by Carroll-Weyl transformations. The resulting worldsheet theory possesses three first-class constraints, C1 = P2, C2 = P · X', and C3 = P · X, whose modes realize a Weyl-BMS algebra. The additional Carroll-Weyl constraint qualitatively changes the quantum gauge complex: its scalar s-ghost is intrinsically coupled to the BMS bc-ghost sector, and the anomaly analysis involves three independent cocycles rather than a single Virasoro-type central charge. Starting from the gauge-fixed action, we derive the complete Faddeev-Popov complex, construct the matter and ghost currents and the BRST charge, and evaluate their equal-time operator products in the flipped, equivalently highest-weight, representation. The matter and ghost anomaly coefficients are (cLL,cLS,cSS)matter=(2D,−D,−D) and (cLL,cLS,cSS)ghost=(−54,6,4). Because the corresponding central terms multiply linearly independent ghost bilinears in QB2, BRST nilpotency requires the three conditions D=27, D=6, and D=4, respectively. These conditions are mutually incompatible. Consequently, there is no target-space dimension in which the minimal flat Carroll-Weyl matter-plus-ghost complex is anomaly-free in the highest-weight representation. The familiar D=26 condition of the ILST null string is recovered only after truncation to the two-constraint BMS subsector, which defines a different quantum gauge complex.
Related
- Reflected constraint algebras of open Carroll--Weyl null strings
- A note on the BRST-BV Formalism Explanation of Deformation Quantization and Algebraic Index Theorem
- Covariant Phase Space and Carroll-Weyl χ Symmetry of Carroll Non-BPS Dp-branes
- Classical Shadows of Higher-Form BRST Anomalies
- Holonomies and Boundary Symmetries in the Discrete BF Formulation of Carroll Dilaton Gravity
BibTeX
@misc{duary2026brst,
title = {{BRST quantization of Carroll-Weyl gauged null strings}},
author = {Sarthak Duary and Sourav Maji},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2608.02731},
eprint = {2608.02731},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.02731},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - BRST quantization of Carroll-Weyl gauged null strings
AU - Sarthak Duary
AU - Sourav Maji
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2608.02731
UR - https://arxiv.org/abs/2608.02731
AB - We study the BRST quantization of the null string after completing its local gauge symmetry by Carroll-Weyl transformations. The resulting worldsheet theory possesses three first-class constraints, C_1 = P^2, C_2 = P · X', and C_3 = P · X, whose modes realize a Weyl-BMS algebra. The additional Carroll-Weyl constraint qualitatively changes the quantum gauge complex: its scalar s-ghost is intrinsically coupled to the BMS bc-ghost sector, and the anomaly analysis involves three independent cocycles rather than a single Virasoro-type central charge. Starting from the gauge-fixed action, we derive the complete Faddeev-Popov complex, construct the matter and ghost currents and the BRST charge, and evaluate their equal-time operator products in the flipped, equivalently highest-weight, representation. The matter and ghost anomaly coefficients are (c_LL,c_LS,c_SS)_matter=(2D,−D,−D) and (c_LL,c_LS,c_SS)_ghost=(−54,6,4). Because the corresponding central terms multiply linearly independent ghost bilinears in Q_B^2, BRST nilpotency requires the three conditions D=27, D=6, and D=4, respectively. These conditions are mutually incompatible. Consequently, there is no target-space dimension in which the minimal flat Carroll-Weyl matter-plus-ghost complex is anomaly-free in the highest-weight representation. The familiar D=26 condition of the ILST null string is recovered only after truncation to the two-constraint BMS subsector, which defines a different quantum gauge complex.
ER -