AI 中文总结
研究重轻维拉索罗块，通过将经典单值性方法与体几何联系，表明单值性矩阵特征向量编码体测地线端点，得出相关方程，还从欧几里得几何重推，计算了非真空 5 点 HHLLL 块，给出从体计算重轻块的通用框架及可计算性阈值。
AI 中文摘要
AdS/CFT 对应将反德西特空间中的引力与边界共形场论联系起来，在 AdS₃/CFT₂情形下，边界理论的维拉索罗对称性将关联函数组织成共形块。在半经典极限下，这些块由体中的测地线网络长度计算得出，在重轻区域最为明显，其中重算子产生背景由轻算子探测。我们将经典单值性方法与全息坐标中的体几何联系起来，表明单值性矩阵的特征向量编码体测地线的端点。这产生了轻作用和确定内部测地线网络的方程；关键是，内部网络方程与重背景无关。对于两个重算子，我们从基本欧几里得几何重新推导相同的方程，这提供了一个独立的几何检验。作为应用，我们计算了完整的非真空 5 点 HHLLL 块，目前仅在超轻近似中已知。更广泛地说，我们的构造给出了一个从体计算重轻块的通用框架，同时确定其可计算性的阈值。
英文摘要
The AdS/CFT correspondence relates gravity in anti-de Sitter space to a boundary conformal field theory, and in its AdS$_3$/CFT$_2$ instance the Virasoro symmetry of the boundary theory organizes correlation functions into conformal blocks. In the semiclassical limit these blocks are computed by lengths of geodesic networks in the bulk, most sharply in the heavy-light regime, where heavy operators source a background probed by light ones. We relate the classical monodromy method to this bulk geometry in holographic coordinates, showing that the eigenvectors of the monodromy matrix encode the endpoints of bulk geodesics. This yields the light action and the equations determining the internal geodesic network; crucially, the internal network equations are independent of the heavy background. For two heavy operators we rederive the same equations from elementary Euclidean geometry, which provides an independent geometric check. As an application we compute the full non-vacuum 5-point HHLLL block, so far known only in the superlight approximation. More broadly, our construction gives a general framework for computing heavy-light blocks from the bulk, while at the same time fixing its threshold of computability.
Comments15 pages
