AI 中文总结
本文采用物理引导符号回归方法，得到ABJM理论有效扭曲超势的精确模完备闭式，其微扰部分和IIA型亏格展开具有特定结构，可复现高精度数值数据。
AI 中文摘要
有效扭曲超势支配三维𝒩=2理论在Cardy极限下的超对称配分函数，以及大N时拼接成超对称AdS₄黑洞熵函数的引力块。我们采用机器学习发现流程——带整数关系检测的物理引导符号回归——应用于多达800位的Bethe真空数据，确定了通用扭曲下U(N)ₖ×U(N)₋ₖ ABJM理论的壳上结构。其微扰部分仅含两项：移位秩的3/2次幂项和与N无关的常数映射，我们对每个整数阶都得到了闭式形式。其IIA型亏格展开在任意亏格下都存在闭式系数公式，涉及二项式和伯努利数项，且具有渐近性。对于k=1、2、4，整个有限N余项是单个绝对收敛的除子求和q级数，通过将一阶微分算子作用于Γ₀(2)或Γ₀(4)上权为4的艾森斯坦级数的艾克勒积分得到，该闭式形式可复现数据至约10⁻⁷⁹⁷的精度。
英文摘要
The effective twisted superpotential governs the supersymmetric partition functions of three-dimensional $\mathcal{N}=2$ theories in the Cardy limit and, at large $N$, the gravitational blocks that are glued into the entropy function of supersymmetric $\mathrm{AdS}_4$ black holes. We determine its on-shell structure for $\mathrm{U}(N)_k\times\mathrm{U}(N)_{-k}$ ABJM theory at the universal twist, using a machine-learning discovery pipeline---physics-informed symbolic regression with integer-relation detection---applied to Bethe-vacuum data of up to $800$ digits. Its perturbative part terminates after two terms, a shifted-rank $3/2$-power and an $N$-independent constant map, which we obtain in closed form for every integer level. Its type-IIA genus expansion admits a closed coefficient formula at arbitrary genus, involving binomial and Bernoulli-number terms, and is asymptotic. For $k=1,2,4$ the entire finite-$N$ remainder is a single absolutely convergent divisor-sum $q$-series, obtained by applying a first-order differential operator to the Eichler integral of a weight-four Eisenstein series on $Γ_0(2)$ or $Γ_0(4)$. This closed form reproduces the data to $\sim\!10^{-797}$.
Comments9 pages, 4 figures
