Quantum anomalies of tensionless bosonic strings

A

bstract

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 [1], the D -dimensional ILST null string [2], the D -dimensional Carroll-Weyl gauged string [3, 4], and the D -dimensional hybrid null string [5]. 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

. 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.