标题： 对称模空间的边界与渐近区域猜想 显示英文标题

标题： The Boundary of Symmetric Moduli Spaces and the Swampland Distance Conjecture

摘要： 对于非紧致的局部对称模空间M，测地线集合和边界几何可以通过群论完全表征。 特别是，渐近于给定无限距离边界点的测地线由局部等距群G的一个有理抛物子群P(Q)以及P(Q)的Cartan子代数中的一个元素来表征。 在假设M满足arXiv:2412.03640中的“可紧化”约束以及关于状态谱的一些温和条件的情况下，我们使用这个形式化方法证明了几乎所有局部对称空间M的Swampland距离猜想。我们表明，这些状态必然在G的某个表示中变换，并且进一步表明编码主导态塔变轻的指数速率的凸包仅仅是该表示权重的凸包。 在一篇配套论文中，我们随后使用该形式化方法对所有与Emergent String猜想一致的局部对称空间和不可约表示进行分类。 显示英文摘要

摘要： For non-compact, locally symmetric moduli spaces M, the set of geodesics and the geometry of the boundary can be completely characterised using group theory. In particular, geodesics that asymptote to a given infinite distance boundary point are characterised by a choice of rational parabolic subgroup P(Q) of the local isometry group G and an element of the Cartan subalgebra of P(Q). Under the assumption that M satisfies the "compactifiability" constraint of arXiv:2412.03640 and some mild conditions on the spectrum of states, we use this formalism to prove the Swampland Distance Conjecture for essentially all locally symmetric spaces M. We show that the states necessarily transform in some representation of G, and further that the convex hull encoding the exponential rate at which the leading tower of states becomes light is simply the convex hull of the weights of the representation. In a companion paper, we then use the formalism to classify all locally symmetric spaces and irreducible representations that are consistent with the Emergent String Conjecture.