论文标题
穿越桥梁的桥桥限制了定理
Crossing bridges with strong Szego limit theorem
论文作者
论文摘要
我们开发了一种新技术，用于计算平面n = 4 Sym理论中重型半BP运算符的一类四点相关函数，该功能将分解为具有任意桥梁长度的两个八角形形式的产物。我们表明，八角形可以表示为可集成的贝塞尔操作员的弗雷德霍尔姆决定因素，并证明这种表示在弱耦合和强耦合处都非常有效地找到八块。在弱耦合下，当四个半BP的操作员以顺序分离的方式分离时，八角形遵守Toda晶格方程，可以以封闭形式找到。在强耦合时，我们利用强szego限制定理来得出八角形的领先渐近行为，然后使用微分方程的方法来确定剩余的强耦合扩展的转向式术语，从而在逆耦合中的任何顺序。为了实现这一目标，我们将文献中可用的结果推广到贝塞尔运营商决定因素的渐近行为。作为我们分析的副产品，我们为贝塞尔操作员的决定因素制定了一种szego-akhiezer-kac公式，并具有Fisher-hartwig奇异性，并开发了一种系统的方法来说明抑制电力的贡献。
We develop a new technique for computing a class of four-point correlation functions of heavy half-BPS operators in planar N=4 SYM theory which admit factorization into a product of two octagon form factors with an arbitrary bridge length. We show that the octagon can be expressed as the Fredholm determinant of the integrable Bessel operator and demonstrate that this representation is very efficient in finding the octagons both at weak and strong coupling. At weak coupling, in the limit when the four half-BPS operators become null separated in a sequential manner, the octagon obeys the Toda lattice equations and can be found in a closed form. At strong coupling, we exploit the strong Szego limit theorem to derive the leading asymptotic behavior of the octagon and, then, apply the method of differential equations to determine the remaining subleading terms of the strong coupling expansion to any order in the inverse coupling. To achieve this goal, we generalize results available in the literature for the asymptotic behavior of the determinant of the Bessel operator. As a byproduct of our analysis, we formulate a Szego-Akhiezer-Kac formula for the determinant of the Bessel operator with a Fisher-Hartwig singularity and develop a systematic approach to account for subleading power suppressed contributions.
