论文标题
$χ$ cft $ _4 $中的可解决的单条跟踪四点相关器
Exactly solvable single-trace four point correlators in $χ$CFT$_4$
论文作者
论文摘要
在本文中，我们研究了手性形式的共同场理论（$χ$ cft $ _4 $）中的一类平面单轨四点相关器，作为$γ$ formed $ \ mathcal {n} = 4 $ sysey的双缩放限制。在平面（t'hooft）限制中，每一个相关器都通过一个feynman的积分来描述，具有正方形晶格“渔网”和/或Yukawa顶点的蜂窝状晶格的大量拓扑。通过$（1,5）$对称性的确切可溶解的自旋链磁体来实现此类Feynmann积分的计算。在本文中，我们详细解释了我们最近的字母中介绍的磁体模型的解，并获得了代表磁铁分离变量频谱上的Feynman积分的一般公式，用于相应的相关器中的任何数量的标量和费米语场。仅对于标量场的特殊选择，我们的公式就可以繁殖B. b. b. b. b. b. b. b. and L. dixon对渔网积分的猜想。
In this paper we study a wide class of planar single-trace four point correlators in the chiral conformal field theory ($χ$CFT$_4$) arising as a double scaling limit of the $γ$-deformed $\mathcal{N}=4$ SYM theory. In the planar (t'Hooft) limit, each of such correlators is described by a single Feynman integral having the bulk topology of a square lattice "fishnet" and/or of an honeycomb lattice of Yukawa vertices. The computation of this class of Feynmann integrals at any loop is achieved by means of an exactly-solvable spin chain magnet with $SO(1,5)$ symmetry. In this paper we explain in detail the solution of the magnet model as presented in our recent letter and we obtain a general formula for the representation of the Feynman integrals over the spectrum of the separated variables of the magnet, for any number of scalar and fermionic fields in the corresponding correlator. For the particular choice of scalar fields only, our formula reproduces the conjecture of B. Basso and L. Dixon for the fishnet integrals.
