AI 中文总结
本文通过Schwinger-Dyson方程检验纯开放矩阵-张量模型对三维引力的描述，发现特定计数规则与猜想一致，并强调路径积分中体拓扑集合的指定至关重要。
AI 中文摘要
我们利用Schwinger-Dyson关系在纯开放扇区检验了所提出的三维引力的矩阵-张量描述。我们对柱面振幅的拓扑贡献进行了枚举和分类。在由Virasoro TQFT启发的提议计数规则下，我们发现与势中两个相互作用项相关的贡献流形数量之间的猜想单位差一致。相反，若分别对所有不等价的曲面嵌入进行计数，则会得到不匹配的结果。这一比较强调了在引力路径积分中明确指定所包含的体拓扑集合的重要性。
英文摘要
We test the proposed matrix-tensor description of three-dimensional gravity using a Schwinger-Dyson relation in its purely open sector. We enumerate and classify the topological contributions to a cylinder amplitude. Under a proposed counting prescription motivated by Virasoro TQFT, we find agreement with the conjectured unit difference between the numbers of contributing manifolds associated to the two interaction terms in the potential. By contrast, counting all inequivalent surface embeddings separately would instead give a mismatch. This comparison highlights the importance of specifying the set of bulk topologies to be included in the gravitational path integral.
Comments21 pages + appendices
