Quantum Anomalies of Tensionless Bosonic Strings

2026/08/04 by Bin Chen, Zezhou Hu
Physics and Astronomy · #hep-th

paper · pdf

30 pages, 4 appendices

arxiv created 2026/08/04 · arxiv updated 2026/08/05

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 \citeGustafsson:1994kr, the D-dimensional ILST null string \citeIsberg:1993av, the D-dimensional Carroll-Weyl gauged string \citeSheikh-Jabbari:2026vqh, Sheikh-Jabbari:2026tpf, and the D-dimensional hybrid null string \citeChen: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 d_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.

Citations

• BRST quantization of Carroll-Weyl gauged null strings
• Tensionless Strings from Worldsheet Symmetries
• On BMS Invariance of Gravitational Scattering
• Tensionless Strings and Galilean Conformal Algebra
• Flat limit of three dimensional asymptotically anti–de Sitter spacetimes
• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• The BMS/GCA correspondence
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• Stringy gravity, interacting tensionless strings and massless higher spins
• A general BRST approach to string theories with zeta function regularizations
• Hamiltonian BRST Quantization of the Conformal String
• Strongly Topological Interactions of Tensionless Strings
• Classical and Quantized Tensionless Strings
• String theory beyond the Planck scale
• Classical null strings