标题： 《IIBordia编年史：对偶性、边界态和沼泽地》 显示英文标题

标题： The Chronicles of IIBordia: Dualities, Bordisms, and the Swampland

摘要： 在这项工作中，我们研究了IIB型弦论几何中沼泽地共边猜想的上下文。相当引人注目的是，我们发现许多具有共边束的非平凡共边类，这些共边束位于与费米子相关的Mp$(2,\mathbb{Z})$的双层覆盖SL$(2,\mathbb{Z})$中，对应于众所周知的超对称F理论背景的渐近边界。 这些包括$[p,q]$-7-膜，非希格斯化簇，S-折叠，以及各种低维推广。 这些弦理论对象破坏了与非平凡共边群相关的全局对称性，为共边猜想提供了强有力的测试。 进一步包括世界面取向反转将对偶群提升到GL$(2,\mathbb{Z})$的Pin$^+$覆盖。相应的共边群需要一个新的非超对称“反射7-膜”及其紧致化以确保全局对称性的缺失，从而为非超对称IIB背景下的共边猜想提供了一个有趣的预测。 本工作的主要部分是显式推导涉及的共边群及其生成器，这些生成器对应于明确的弦理论背景的渐近边界。 主要工具是亚当斯谱序列，我们对此提供了详细的介绍。 我们预计相同的技巧可以应用于广泛的场景。 显示英文摘要

摘要： In this work we investigate the Swampland Cobordism Conjecture in the context of type IIB string theory geometries with non-trivial duality bundle. Quite remarkably, we find that many non-trivial bordism classes with duality bundles in Mp$(2,\mathbb{Z})$, a double cover of SL$(2,\mathbb{Z})$ related to fermions, correspond to asymptotic boundaries of well-known supersymmetric F-theory backgrounds. These include $[p,q]$-7-branes, non-Higgsable clusters, S-folds, as well as various lower-dimensional generalizations. These string theoretic objects break the global symmetries associated to the non-trivial bordism groups, providing a strong test of the Cobordism Conjecture. Further including worldsheet orientation reversal promotes the duality group to the Pin$^+$ cover of GL$(2,\mathbb{Z})$. The corresponding bordism groups require a new non-supersymmetric "reflection 7-brane" and its compactifications to ensure the absence of global symmetries, thus providing an interesting prediction of the Cobordism Conjecture for non-supersymmetric type IIB backgrounds. A major component of the present work is the explicit derivation of the involved bordism groups as well as their generators, which correspond to asymptotic boundaries of explicit string theory backgrounds. The main tool is the Adams spectral sequence, to which we provide a detailed introduction. We anticipate that the same techniques can be applied in a wide variety of settings.