arXiv 2409.127862024-09-19hep-th

$\mathcal{N}=4$ 超杨-米尔斯理论中线缺陷关联函数的电磁对偶性

Electromagnetic Duality for Line Defect Correlators in $\mathcal{N}=4$ Super Yang-Mills Theory

Daniele Dorigoni, Zhihao Duan, Daniele R. Pavarini, Congkao Wen, Haitian Xie

备注：: 30 + 21 pages

AI总结：

本文在N=4超杨-米尔斯理论中研究带电磁荷(p,q)的半BPS线缺陷的积分关联函数，引入一类新的实解析自守函数来描述其SL(2,Z)电磁对偶变换，并证明大N展开系数由这些函数的有限线性组合给出，为SU(2)和SU(3)情形提供了显式构造，直接给出非微扰结果。

摘要：

我们研究了在规范群为 $SU(N)$ 的 $\mathcal{N}=4$ 超对称杨-米尔斯理论（SYM）中，由电磁荷 $(p,q)$ 标记的半BPS线缺陷存在时，应力张量多重态的两个超共形初级算符的特定积分关联函数。$\mathcal{N}=4$ SYM 中 ${\rm SL}(2,\mathbb{Z})$ 电磁对偶的一个重要推论是，当复耦合常数 $τ=θ/(2π)+4πi /g_{_{\rm YM}}^2$ 经过适当变换时，具有不同荷 $(p,q)$ 的线缺陷算符的关联函数必须以非平凡的方式相互关联。在这项工作中，我们引入了一类新的实解析函数，其关于 ${\rm SL}(2,\mathbb{Z})$ 的自守性质与 $\mathcal{N}=4$ SYM 中线缺陷算符在电磁对偶下的预期变换相匹配。在大 $N$ 和固定 $τ$ 下，我们考虑的关联函数与全息对偶的 IIB 超弦理论中扩展 $(p,q)$ 弦对两个引力子的散射振幅相关。我们证明，积分两点线缺陷关联函数的大 $N$ 展开系数由这类自守函数元素的具有有理系数的有限线性组合给出。另一方面，对于任何固定的 $N$ 值，我们猜想线缺陷积分关联函数可以表示为这类自守函数的形式无穷级数。该级数的重求和产生线缺陷积分关联函数的简单格点求和表示，该表示体现了其自守性质。我们明确地展示了规范群为 $SU(2)$ 和 $SU(3)$ 的情况下的构造。我们的结果直接给出了存在 't Hooft 线缺陷时的非微扰积分关联函数，这些可观测量通过其他方法很难计算。

英文摘要：

We study particular integrated correlation functions of two superconformal primary operators of the stress tensor multiplet in the presence of a half-BPS line defect labelled by electromagnetic charges $(p,q)$ in $\mathcal{N}=4$ supersymmetric Yang-Mills theory (SYM) with gauge group $SU(N)$. An important consequence of ${\rm SL}(2,\mathbb{Z})$ electromagnetic duality in $\mathcal{N}=4$ SYM is that correlators of line defect operators with different charges $(p,q)$ must be related in a non-trivial manner when the complex coupling $τ=θ/(2π)+4πi /g_{_{\rm YM}}^2$ is transformed appropriately. In this work we introduce a novel class of real-analytic functions whose automorphic properties with respect to ${\rm SL}(2,\mathbb{Z})$ match the expected transformations of line defect operators in $\mathcal{N}=4$ SYM under electromagnetic duality. At large $N$ and fixed $τ$, the correlation functions we consider are related to scattering amplitudes of two gravitons from extended $(p,q)$-strings in the holographic dual type IIB superstring theory. We show that the large-$N$ expansion coefficients of the integrated two-point line defect correlators are given by finite linear combinations with rational coefficients of elements belonging to this class of automorphic functions. On the other hand, for any fixed value of $N$ we conjecture that the line defect integrated correlators can be expressed as formal infinite series over such automorphic functions. The resummation of this series produces a simple lattice sum representation for the integrated line defect correlator that manifests its automorphic properties. We explicitly demonstrate this construction for the cases with gauge group $SU(2)$ and $SU(3)$. Our results give direct access to non-perturbative integrated correlators in the presence of an 't Hooft-line defect, observables otherwise very difficult to compute by other means.

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