标题： 边界和膜的自举 显示英文标题

标题： Bootstrapping Boundaries and Branes

摘要： 二维共形场论（CFT）的共形边界条件的研究有着悠久的历史，从一维量子链中杂质的描述到弦理论中D-膜的表述，涵盖了广泛的主题。 然而，共形边界的图景在很大程度上仍不为人所知，即使是在局部算符数据完全确定的有理CFT中也是如此。 我们通过研究环面配分函数在相同边界条件下的开闭一致性条件所引出的约束方程，系统地启动了对二维CFT中共形边界的bootstrap研究。 我们发现，这个看似简单的bootstrap方程，结合单位性，对可容许的边界态施加了令人惊讶的强大限制。 特别是，我们推导出了稳定边界条件张力（边界熵）的普适界限，这些界限为潜在的D-膜衰变提供了严格的诊断工具。 我们还在若干有理CFT中找到了稳定膜的bootstrap问题的独特解。 在此过程中，我们观察到了环面bootstrap与球体填充问题之间的一个有趣联系，这是之前关于模群bootstrap工作的自然延伸。 我们还得到了大中心电荷下边界熵的界限。 这些结果可能对AdS$_3$中纯引力的世界终结膜有影响。 显示英文摘要

摘要： The study of conformal boundary conditions for two-dimensional conformal field theories (CFTs) has a long history, ranging from the description of impurities in one-dimensional quantum chains to the formulation of D-branes in string theory. Nevertheless, the landscape of conformal boundaries is largely unknown, including in rational CFTs, where the local operator data is completely determined. We initiate a systematic bootstrap study of conformal boundaries in 2d CFTs by investigating the bootstrap equation that arises from the open-closed consistency condition of the annulus partition function with identical boundaries. We find that this deceivingly simple bootstrap equation, when combined with unitarity, leads to surprisingly strong constraints on admissible boundary states. In particular, we derive universal bounds on the tension (boundary entropy) of stable boundary conditions, which provide a rigorous diagnostic for potential D-brane decays. We also find unique solutions to the bootstrap problem of stable branes in a number of rational CFTs. Along the way, we observe a curious connection between the annulus bootstrap and the sphere packing problem, which is a natural extension of previous work on the modular bootstrap. We also derive bounds on the boundary entropy at large central charge. These potentially have implications for end-of-the-world branes in pure gravity on AdS$_3$.