AI 中文总结
本文研究AdS_D庞加莱片中Carroll-Weyl规范零弦的BRST量子化，分析其剩余代数的中心扩张，在正则最高权一阶表示中得到Virasoro型中心扩张，对应非平凡BRST上闭链抵消给出D=27，且与极小平直Carroll-Weyl理论结构不同。
AI 中文摘要
我们研究了AdS_D的庞加莱片中的Carroll-Weyl规范零弦及其BRST量子化。在庞加莱坐标X^A=(z,x^i)中，径向共形 Killing 矢量K=∂_z在适当的共形相关标架中成为同调矢量。对同调哈密顿量约束进行依赖于场的重标度，得到径向适配基：ℳ=1/2(P_z²+P_iP^i)、ℒ=-P_AX'^A和𝒮=P_z，其中ℳ沿Carroll-Weyl径向流不变。它们的模式形成由阿贝尔权1流扩展的BMS₃代数。我们对该剩余代数允许的中心扩张进行分类，发现LL、LM、LS和SS通道中有四个独立的上同调类。随后构造了相关的BRST复形，包括径向Carroll-Weyl约束的鬼对。在正则最高权一阶表示中，仅实现了Virasoro型中心扩张：(c_LL,c_LM,c_LS,c_SS)=(2D-54,0,0,0)。因此，对应非平凡BRST上闭链的抵消在该表示中给出D=27。这在结构上不同于极小平直Carroll-Weyl理论，后者中膨胀约束X·P会产生额外的反常通道。
英文摘要
We study the Carroll-Weyl gauged null string in the Poincaré patch of $\mathrm{AdS}_D$ and its BRST quantization. In Poincaré coordinates $X^A=(z,x^i)$, the radial conformal Killing vector $K=\partial_z$ becomes homothetic in a suitable conformally related frame. A field-dependent rescaling of the homothetic Hamiltonian constraint then leads to the radial-adapted basis $\mathcal{M}=\frac{1}{2}(P_z^2+P_iP^i)$, $\mathcal{L}=-P_AX'^A$, and $\mathcal{S}=P_z$, with $\mathcal{M}$ invariant along the Carroll-Weyl radial flow. Their modes form a $\mathrm{BMS}_3$ algebra extended by an abelian weight-one current. We classify the central extensions allowed by this residual algebra and find four independent cohomology classes in the $LL$, $LM$, $LS$, and $SS$ channels. We then construct the associated BRST complex, including the ghost pair for the radial Carroll-Weyl constraint. In the canonical highest-weight first-order representation, only the Virasoro-type central extension is realized: $(c_{LL},c_{LM},c_{LS},c_{SS})=(2D-54,0,0,0)$. Cancellation of the corresponding nontrivial BRST cocycle therefore gives $D=27$ in this representation. This differs structurally from the minimal flat Carroll-Weyl theory, where the dilation constraint $X\cdot P$ gives extra anomaly channels.
Comments35+21 pages, 3 figures
