Quantum Anomalies of Tensionless Bosonic Strings
Abstract
We systematically investigate and compare the worldsheet actions, BRST structures and the quantum anomalies of four different formulations of tensionless (T = 0) bosonic string theory: the (D+2)-dimensional conformal string \cite{Gustafsson:1994kr}, the D-dimensional ILST null string \cite{Isberg:1993av}, the D-dimensional Carroll-Weyl gauged string \cite{Sheikh-Jabbari:2026vqh, Sheikh-Jabbari:2026tpf}, and the D-dimensional hybrid null string \cite{Chen:2026klv}. By expressing all fields and constraint generators strictly in terms of mode expansions and adopting a unified algebraic framework, we analyze their quantum anomalies under two distinct worldsheet vacua: the induced vacuum and the flipped vacuum. With the BRST-compatible vacuum definition and the symmetric α=0 zeta prescription, we show that no critical dimension is inferred from the vanishing of the quantum anomaly in the induced vacuum. In contrast, the flipped highest-weight vacuum leads to non-trivial constraints, reproducing the critical dimension D=26 for the ILST null strings, a λ-dependent critical dimension D(λ) for the hybrid null string whose range covers every positive integer D≥ 4 (reproduces D=26 at λ=1), and more importantly showing that the conformal string and the Carroll-Weyl gauged string are structurally anomalous with no consistent critical dimension due to the discrepancy of their central charge parameters d̃i. Furthermore, the ILST null string model has target-space conformal symmetry SO(D,2), the ghost-completed SO(D,2) charges are closed on the induced-vacuum BRST cohomology in the α=0 prescription, whereas the symmetry is quantum mechanically broken in the flipped vacuum.
Related
- TT̅ correlators from tensionless strings
- TT̅ correlators from tensionless strings
- From closed to open strings: The tensionless route in Kalb-Ramond background and noncommutativity
- Tensionless limit of M5-brane and conformal symmetry of its bosonic body
- Path integral quantization of null bosonic strings with Carroll-Weyl ghosts
BibTeX
@misc{chen2026quantum,
title = {{Quantum Anomalies of Tensionless Bosonic Strings}},
author = {Bin Chen and Zezhou Hu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.02987},
eprint = {2608.02987},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.02987},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Anomalies of Tensionless Bosonic Strings
AU - Bin Chen
AU - Zezhou Hu
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2608.02987
UR - https://arxiv.org/abs/2608.02987
AB - We systematically investigate and compare the worldsheet actions, BRST structures and the quantum anomalies of four different formulations of tensionless (T = 0) bosonic string theory: the (D+2)-dimensional conformal string \cite{Gustafsson:1994kr}, the D-dimensional ILST null string \cite{Isberg:1993av}, the D-dimensional Carroll-Weyl gauged string \cite{Sheikh-Jabbari:2026vqh, Sheikh-Jabbari:2026tpf}, and the D-dimensional hybrid null string \cite{Chen:2026klv}. By expressing all fields and constraint generators strictly in terms of mode expansions and adopting a unified algebraic framework, we analyze their quantum anomalies under two distinct worldsheet vacua: the induced vacuum and the flipped vacuum. With the BRST-compatible vacuum definition and the symmetric α=0 zeta prescription, we show that no critical dimension is inferred from the vanishing of the quantum anomaly in the induced vacuum. In contrast, the flipped highest-weight vacuum leads to non-trivial constraints, reproducing the critical dimension D=26 for the ILST null strings, a λ-dependent critical dimension D(λ) for the hybrid null string whose range covers every positive integer D≥ 4 (reproduces D=26 at λ=1), and more importantly showing that the conformal string and the Carroll-Weyl gauged string are structurally anomalous with no consistent critical dimension due to the discrepancy of their central charge parameters d̃_i. Furthermore, the ILST null string model has target-space conformal symmetry SO(D,2), the ghost-completed SO(D,2) charges are closed on the induced-vacuum BRST cohomology in the α=0 prescription, whereas the symmetry is quantum mechanically broken in the flipped vacuum.
ER -