平面N = 4超杨-米尔斯中奇数共形自旋下的次下领先阶BFKL本征值
The next-to-next-to-leading order BFKL eigenvalue at odd conformal spin in planar N=4 super Yang-Mills
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中文总结 AI 辅助
研究平面N = 4超杨-米尔斯中奇数共形自旋下的三圈BFKL本征值，通过直接梅林提取精确获取原子表，给出系数形式，在ν = 0时截距可重现量子谱曲线值，本征值无乘积形式，配套论文有推导和完整表达式。
中文摘要 AI 辅助
我们以封闭形式给出了平面N = 4超杨-米尔斯在奇数共形自旋n下的三圈（次下领先阶）BFKL本征值，它是嵌套调和和与z = (|n| - 1)/2 + i ν的有理函数的有限组合。对于每个奇数n >= 3，通过直接梅林提取从Caron - Huot - Herranen三圈积分中精确提取原子表。系数是1、π²和ζ₃的有理倍数。在固定基下，47个系数槽中的40个以两个阶梯距离的调和和形式闭合。在ν = 0时，截距逐自旋重现独立量子谱曲线值直至n = 91。每个奇数自旋下本征值严格无乘积形式。在配套论文中给出了推导和完整表达式。
英文摘要
We give the next-to-next-to-leading order color-singlet BFKL eigenvalue of planar N=4 super Yang-Mills at odd conformal spin n in closed form. At the two lower orders the known expressions contain nested harmonic sums only at the two conjugate points z=(|n|-1)/2+i nu and zbar. At three loops the sums are evaluated on a ladder of integer-shifted arguments from the reflected point -zbar up to z, with one point past it, the coefficient at a rung fixed by its two distances to the ends. Seven families are the exception, their coefficients written through ladder sums whose summand shifts with the summation index. For one of the seven the coefficient lies outside the fixed-coefficient algebra of nested harmonic sums of the two distances, an arithmetic obstruction in the denominators. That exclusion reaches the eigenvalue coefficient only through an agreement of rule and coefficient verified and not proved. Rules uniform in the conformal spin produce all forty-seven families at every odd n>=3; no per-spin coefficient is tabulated in the closed form, and the n=1 boundary block is supplied separately. Those rules are a reconstruction from the computed spins, exact at every one of them, verified over the range n<=99 and at the holdout spin n=101, and not proved at arbitrary odd n. Each atom-table coefficient is a rational combination of 1, pi^2 and zeta_3, coefficient and atom together carrying transcendental weight five. Along nu=0 the intercepts match the Quantum Spectral Curve values at each computed odd spin through n=91, the extent of those values. The comparison tests the integrand and the reduction together at one point of each spin, for most of them for the first time. Away from that line the closed form gives the collinear behavior of the block uniformly in the spin, which the intercepts alone do not fix.
发表机构
- Ariel University（阿里埃尔大学）
机构由 AI 辅助整理，请以论文原文为准。
