论文标题
在广义渔网和手性鱼网理论中振幅
Regge amplitudes in Generalized Fishnet and Chiral Fishnet Theories
论文作者
论文摘要
我们扩展了\ cite {Chowdhury：2019HNS}的分析，以研究$ 0- $的梅林振幅的轨迹和$ D $ dumensions中广义渔网理论的$ 1- $磁蛋白相关器，以及$ 4 $ dimensions in Chiral Fishnet理论的一种相关器类型。我们开发了一种系统的程序，以扰动研究Regge轨迹并随后执行光谱积分。我们的扰动方法非常通用，原则上可以应用于相关因子，这些相关因子的扰动型轨迹遵循我们列出的某些结构条件。我们的$ d $维度结果减少了以前已知的结果，$ d = 4 $ 0-MAGNON和1-磁杆。作为一项非微不足道的检查，我们表明，使用\ cite {Chowdhury：2019HNS，Korchemsky：2018HNB}评估的1-Magnon相关器的结果与我们的$ d $ dimensional扰动结果非常吻合。我们还扰动地计算手性渔网相关器$ \ langle {香本文开发的技术。由于此相关器具有两个耦合$κ$和$ω$，因此我们获得了封闭形式的限制$κ\至0，ω\至0 $，而$κ/ω$保持常数。我们通过独立的计算方法来验证此计算并获得完美的一致性。
We extend the analysis of \cite{Chowdhury:2019hns} to study the Regge trajectories of the Mellin amplitudes of the $0-$ and $1-$ magnon correlators of the generalized Fishnet theory in $d$ dimensions and one type of correlators of chiral fishnet theory in $4$ dimensions. We develop a systematic procedure to perturbatively study the Regge trajectories and subsequently perform the spectral integral. Our perturbative method is very generic and in principle can be applied to correlators whose perturbative Regge trajectories obey some structural conditions which we list down. Our $d$ dimensional results reduce to previously known results in $d=4$ for 0-magnon and 1- magnon. As a non trivial check, we show that the results for 1-magnon correlator in $d=8$, when evaluated using the exact techniques in \cite{Chowdhury:2019hns, Korchemsky:2018hnb} are in perfect agreement with our $d$ dimensional perturbative results. We also perturbatively compute the Regge trajectories and Regge-Mellin amplitudes of the chiral fishnet correlator $\langle{\rm Tr}[ϕ_1(x_1)ϕ_1(x_2)]{\rm Tr}[ϕ_1^\dagger(x_3)ϕ_1^\dagger(x_4)]\rangle$ using the techniques developed in this paper. Since this correlator has two couplings $κ$ and $ω$, we have obtained closed-form results in the limit $κ\to 0, ω\to 0$ with $κ/ω$ held constant. We verify this computation with an independent method of computing the same and obtain perfect agreement.
