AI 中文总结
本文对经卡罗尔-外尔变换完善规范对称性的零弦开展BRST量子化，发现其反常分析需满足三个互斥的维度条件，不存在使该理论无反常的靶空间维度，仅截断为BMS子sector时可恢复ILST零弦的D=26条件。
AI 中文摘要
我们在通过卡罗尔-外尔变换完善零弦的定域规范对称性后，对其开展BRST量子化研究。所得世界面理论具有三个第一类约束：$C_1 = P^2$、$C_2 = P \cdot X'$、$C_3 = P \cdot X$，其模式实现外尔-BMS代数。额外的卡罗尔-外尔约束从本质上改变了量子规范复形：其标量s-鬼（s-ghost）与BMS bc-鬼（bc-ghost） sector耦合，反常分析涉及三个独立上同调类而非单一Virasoro型中心电荷。我们从规范固定作用量出发，推导完整Faddeev-Popov复形，构造物质流、鬼流及BRST荷，并在翻转的、等价于最高权的表示中计算其等时算子乘积。物质与鬼的反常系数分别为$(c_{LL},c_{LS},c_{SS})_{\text{物质}}=(2D,-D,-D)$和$(c_{LL},c_{LS},c_{SS})_{\text{鬼}}=(-54,6,4)$。由于对应中心项在$Q_B^2$中乘以线性无关的鬼双线性项，BRST幂零性要求$D=27$、$D=6$、$D=4$三个条件，三者互不相容。因此，不存在靶空间维度使得最小平直卡罗尔-外尔物质加鬼复形在最高权表示中无反常。仅当截断为双约束BMS子sector（定义不同量子规范复形）时，才可恢复ILST零弦熟知的$D=26$条件。
英文摘要
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, $C_1 = P^2$, $C_2 = P \cdot X'$, and $C_3 = P \cdot X$, 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 $(c_{LL},c_{LS},c_{SS})_{\mathrm{matter}}=(2D,-D,-D)$ and $(c_{LL},c_{LS},c_{SS})_{\mathrm{ghost}}=(-54,6,4)$. 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.
Comments39+18 pages
