论文标题
探索T^d上的异性弦的景观
Exploring the landscape of heterotic strings on T^d
论文作者
论文摘要
T^d上的杂弦的压缩是最简单，最丰富的操场，可以发现swampland的想法：u（1）^{d+16}左移动量规对称性在模仿空间中的特殊点上只能增强到某些群体。我们根据晶格嵌入技术说明标准，以确定是否实现了量规组。对于通用D，我们进一步展示了如何通过修改纳兰晶格II_ {1,17}的扩展Dynkin图中删除节点的方法来获取导致给定量规组的模量。还开发了更通用的探索模量空间的算法。对于D = 1和2，我们列出了有关II_ {D，D+16}中嵌入的所有最大增强量规组，模量和其他相关信息。与K3上T^2和F理论的杂种之间的二元性一致，T^2上的所有可能的量规组都匹配椭圆形K3表面的所有可能的ADE类型的奇异纤维。我们还提出了一种简单的方法，可以在二元组下转换模量，并构建与E_8 X E_8和Spin（32）/Z_2异质理论相关的电荷晶格和模量的地图。
Compactifications of the heterotic string on T^d are the simplest, yet rich enough playgrounds to uncover swampland ideas: the U(1)^{d+16} left-moving gauge symmetry gets enhanced at special points in moduli space only to certain groups. We state criteria, based on lattice embedding techniques, to establish whether a gauge group is realized or not. For generic d, we further show how to obtain the moduli that lead to a given gauge group by modifying the method of deleting nodes in the extended Dynkin diagram of the Narain lattice II_{1,17}. More general algorithms to explore the moduli space are also developed. For d=1 and 2 we list all the maximally enhanced gauge groups, moduli, and other relevant information about the embedding in II_{d,d+16}. In agreement with the duality between heterotic on T^2 and F-theory on K3, all possible gauge groups on T^2 match all possible ADE types of singular fibers of elliptic K3 surfaces. We also present a simple method to transform the moduli under the duality group, and we build the map that relates the charge lattices and moduli of the compactification of the E_8 x E_8 and Spin(32)/Z_2 heterotic theories.
