标题： 6d N=(1,0) 超重力的有限景观 显示英文标题

标题： Finite Landscape of 6d N=(1,0) Supergravity

摘要： 我们提出一个自下而上的论点，表明具有八个超电荷的六维量子引力理论中的无质量场的数量是统一有界的。 具体来说，我们证明张量多重态的数量被限制为$T\leq 193$，并且规范群的秩被限制为$r(V)\leq 480$。 鉴于F理论在椭圆CY 3-流形上的紧化是一个子集，这为椭圆CY 3-流形的Hodge数提供了界限：$h^{1,1}({\rm CY_3})\leq 491$，$h^{1,1}({\rm Base})\leq 194$，这些界限由特殊的椭圆CY 3-流形达到。 这证明了我们的界限是精确的，并且进一步支持了弦理论灯柱原理。 这些结果是通过对张量模空间边界的全面检查得出的，表明任何具有$T\neq0$的一致超引力理论都必须在其谱中包含一个对应于“小弦理论”(LST) 或临界杂交弦的BPS弦。 从这种张量分支分析中，我们建立了嵌入在引力理论中的SCFT和LST之间的包含关系。 结合6d SCFT和LST的分类，这就导致了上述界限。 与之前的工作相结合，这确立了$d\geq 6$的超引力景观的有限性。 显示英文摘要

摘要： We present a bottom-up argument showing that the number of massless fields in six-dimensional quantum gravitational theories with eight supercharges is uniformly bounded. Specifically, we show that the number of tensor multiplets is bounded by $T\leq 193$, and the rank of the gauge group is restricted to $r(V)\leq 480$. Given that F-theory compactifications on elliptic CY 3-folds are a subset, this provides a bound on the Hodge numbers of elliptic CY 3-folds: $h^{1,1}({\rm CY_3})\leq 491$, $h^{1,1}({\rm Base})\leq 194$ which are saturated by special elliptic CY 3-folds. This establishes that our bounds are sharp and also provides further evidence for the string lamppost principle. These results are derived by a comprehensive examination of the boundaries of the tensor moduli branch, showing that any consistent supergravity theory with $T\neq0$ must include a BPS string in its spectrum corresponding to a "little string theory" (LST) or a critical heterotic string. From this tensor branch analysis, we establish a containment relationship between SCFTs and LSTs embedded within a gravitational theory. Combined with the classification of 6d SCFTs and LSTs, this then leads to the above bounds. Together with previous works, this establishes the finiteness of the supergravity landscape for $d\geq 6$.