发表机构
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh; Center for High Energy Physics, Peking University（爱丁堡大学数学与麦克斯韦数学研究所; 北京大学高能物理中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推导了光非真空BMS$_3$块在$1/c_{M}$阶的闭式修正，通过全局块截断和边界引力子方法验证，并证明与Virasoro块的超相对论收缩一致。
AI 中文摘要
我们推导了具有四个光外部原场（一般权重）和非真空交换的最高权重BMS$_3$块在$1/c_{M}$阶修正的闭式表达式。在固定$c_L$和所有算子权重的情况下，我们证明了全局扇区以及恰好包含一个非全局生成元$L_{-n}$或$M_{-n}$（其中$n\geq2$）的后代足以达到该阶。这种截断将内在计算简化为全局块及其导数，我们对其贡献在非零交换boost权重$\xi_{p}$下进行了重求和。对于成对相同的外部算子，我们通过在阴影表示中归一化三点函数中引入边界引力子独立地重现了该修正，同时保持交换的两点函数固定。类似的方案也重现了已知的$1/c$阶非真空Virasoro修正。对于相同的外部配置，对具有一个翻转手征表示的Virasoro块进行形式上的超相对论收缩提供了进一步检验：它产生相同的修正，并且我们证明了收缩与在每个固定后代级别提取$1/c_{M}$系数可交换。具有$\xi_{p}=0$的简并交换需要单独的商构造，并且不能作为一般块的光滑极限获得，我们在附录中对此进行了讨论。
英文摘要
We derive a closed expression for the $1/c_{M}$ correction to highest-weight BMS$_3$ blocks with four light external primaries of generic weights and non-vacuum exchange. With $c_L$ and all operator weights held fixed, we prove that the global sector and descendants containing exactly one non-global generator $L_{-n}$ or $M_{-n}$ with $n\geq2$ suffice through this order. This truncation reduces the intrinsic calculation to global blocks and their derivatives, whose contributions we resum for nonzero exchanged boost weight $ξ_{p}$. For pairwise identical external operators, we independently reproduce the correction through the introduction of boundary gravitons in the normalized three-point functions in the shadow representation, while keeping the exchanged two-point function fixed. The analogous prescription also reproduces the known non-vacuum Virasoro correction at order $1/c$. For the same external configuration, a formal ultra-relativistic contraction of Virasoro blocks with one flipped chiral representation provides a further check: it yields the same correction, and we prove that contraction commutes with extraction of the $1/c_{M}$ coefficient at each fixed descendant level. The degenerate exchange with $ξ_{p}=0$ requires a separate quotient construction and is not obtained as a smooth limit of the generic block, which we discuss in the appendix.
Comments29 pages + appendices
