论文标题
分析性延续谐波和纯粹的想象索引在整数值附近
Analytic continuation of harmonic sums with purely imaginary indices near the integer values
论文作者
论文摘要
我们提出了一种简单的代数方法，用于用整数真实或纯粹的虚构索引分析谐波总和接近负和正整数。我们提供了一个数学代码，以在这些整数附近的小参数中精确扩展谐波总和。作为应用程序，我们考虑了ABJM模型中Twist-1运算符异常维度的分析延续，ABJM模型中包含带有纯粹虚构指数的嵌套谐波总和。我们发现，在BFKL样限制中，结果具有与n = 4 sym和qCD相同的单个单一起行为，但是，我们在此模型中没有找到``bfkl pomeron'''eigenvalue的一般表达。对于斜率函数，我们发现与已知的一般结果的扩展完全一致，并对近斜函数的扩展中的前三个扰动项进行了预测。提出的分析延续方法也可以用于嵌套谐波总和的其他概括。
We present a simple algebraic method for the analytic continuation of harmonic sums with integer real or purely imaginary indices near negative and positive integers. We provide a MATHEMATICA code for exact expansion of harmonic sums in a small parameter near these integers. As an application, we consider the analytic continuation of the anomalous dimension of twist-1 operators in ABJM model, which contains the nested harmonic sums with purely imaginary indices. We found that in the BFKL-like limit the result has the same single-logarithmic behavior as in N=4 SYM and QCD, however, we did not find a general expression for the ``BFKL Pomeron'' eigenvalue in this model. For the slope function, we found full agreement with the expansion of the known general result and give predictions for the first three perturbative terms in the expansion of the next-to-slope function. The proposed method of analytic continuation can also be used for other generalization of the nested harmonic sums.
