发表机构
Queen Mary University of London; Uppsala University; Massachusetts Institute of Technology（伦敦大学玛丽女王学院; 乌普萨拉大学; 麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究II型与I型弦理论中$SO(9)$超表示的增长，通过经验公式、有限域上的精细配分函数、拉德马赫求和推导重数及渐近公式，还将该技术应用于普通表示。
AI 中文摘要
我们研究II型和I型弦理论中质量$SO(9)$超表示的增长。首先，我们通过找到指定任意能级出现哪些表示的经验公式来直接开展研究；接着，通过在有限域上计算的精细配分函数，分别针对单个表示到能级501、针对所有表示到能级226，计算其重数。随后，我们围绕精细配分函数的峰值进行积分，推导出任意表示增长的渐近公式。利用拉德马赫（Rademacher）求和，我们可得到表示重数的高精度近似值。与仅从奇数拉德马赫项获得贡献的超弦配分函数不同，任意表示的重数同时包含偶数和奇数项的贡献。最后，我们将相同技术应用于普通表示，其中简化的精细配分函数可实现更高的计算速度和更简洁的渐近近似表达式。
英文摘要
We study the growth of massive $SO(9)$ super-representations in type II and type I string theories. We do this first directly by finding an empirical formula that specifies which representations appear at any level, and then compute the multiplicities from a refined partition function evaluated over finite fields up to level 501 for individual representations, and level 226 for all representations. We then derive asymptotic formulae for the growth of any representation, which are constructed by integrating about the peaks of the refined partition function. Using a Rademacher sum we can find very accurate approximations for the multiplicities of the representations. Unlike the superstring partition function, which only receives contributions from the odd Rademacher terms, the multiplicities for any representation have contributions from both even and odd terms. Finally, we apply the same techniques to the ordinary representations, where a simplified refined partition function allows for better computational speed and simpler expressions for the asymptotic approximations.
Comments50 pages, 15 figures, 17 tables
