无张力玻色弦的量子反常
Quantum Anomalies of Tensionless Bosonic Strings
浏览论文内容
中文总结 AI 辅助
该研究在统一代数框架下对比四种无张力玻色弦的量子反常，发现不同世界面真空下反常行为差异显著，明确了各理论的临界维数性质与靶空间对称性的量子破缺情况。
中文摘要 AI 辅助
我们系统研究并对比了四种不同表述的无张力（$T = 0$）玻色弦理论的世界面作用量、BRST结构与量子反常，这四种理论分别是：$(D+2)$维共形弦（参考文献\textit{Gustafsson:1994kr}）、$D$维ILST类光弦（参考文献\textit{Isberg:1993av}）、$D$维Carroll-Weyl规范弦（参考文献\textit{Sheikh-Jabbari:2026vqh, Sheikh-Jabbari:2026tpf}）以及$D$维混合类光弦（参考文献\textit{Chen:2026klv}）。我们将所有场与约束生成元严格用模展开形式表达，并采用统一的代数框架，在两种不同的世界面真空——诱导真空与翻转真空下分析它们的量子反常。借助与BRST相容的真空定义以及对称的$\boldsymbol{α=0}$ zeta正则化方案，我们证明在诱导真空下，量子反常的消失并不会导出临界维数。与之相反，翻转最高权真空会给出非平凡约束：对于ILST类光弦，可重现临界维数$D=26$；对于混合类光弦，可得到依赖于$\boldsymbol{λ}$的临界维数$D(λ)$，其取值范围覆盖所有满足$D\boldsymbol{≥4}$的正整数（当$\boldsymbol{λ=1}$时重现$D=26$）；更重要的是，共形弦与Carroll-Weyl规范弦存在结构性反常，由于其中心荷参数$\tilde d_i$存在差异，不存在自洽的临界维数。此外，ILST类光弦模型具有靶空间共形对称性$SO(D,2)$，在$\boldsymbol{α=0}$正则化方案下，补充鬼场后的$SO(D,2)$荷在诱导真空的BRST上同调上是闭合的，而该对称性在翻转真空中会发生量子力学破缺。
英文摘要
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 $D\geq 4$ (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 $\tilde d_i$. 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.
