AI 中文总结
该研究确定了ABJM理论、ADHM理论相关配分函数的N无关常数项，通过检验并填补超对称配分函数全阶1/N展开的未确定部分，完善了场论及对偶量子引力描述的相关结果。
AI 中文摘要
我们精确确定了ABJM理论的拓扑扭转指数及相关Bethe势的全阶1/N展开中与N无关的常数项，同时确定了ADHM理论的Bethe势常数。我们通过高精度Bethe-Ansatz数值方法解析重构这些常数，验证其直至非微扰修正层面，发现它们与控制圆三球配分函数的常映射函数A密切相关。ADHM和ABJM常数的表达式通过了3d镜像对称性所要求的非平凡检验，且通过新近建立的因式分解关系，还能精确确定压扁三球配分函数在其大压扁度展开中前两个主导阶的与N无关的常数贡献。这些常数恰好填补了近期3d超对称配分函数全阶1/N展开精确结果中未确定的部分，从而为完善场论及其对偶量子引力描述中的相关结果迈出了重要一步。
英文摘要
We determine in closed form the $N$-independent constant terms in the all-order $1/N$ expansions of the topologically twisted index and of the associated Bethe potential for the ABJM theory, as well as the Bethe potential constant of the ADHM theory. We reconstruct these constants analytically from high-precision Bethe-Ansatz numerics, verify them down to the level of non-perturbative corrections, and find them to be closely related to the constant map function $A$ governing the round three-sphere partition function. The resulting expressions for the ADHM and ABJM constants pass the non-trivial test dictated by 3d mirror symmetry. Via recently established factorization relations, they also determine in closed form the $N$-independent constant contribution to the squashed three-sphere partition function, through the first two leading orders in its large-squashing expansion. These constants supply precisely the piece left undetermined in the recent exact results for 3d supersymmetric partition functions to all orders in the $1/N$ expansion, and thereby mark an important step toward completing them, both in field theory and in the dual quantum gravity description.
Commentsv1: 18 pages
