arXiv 0809.16322008-09hep-thhep-ph

Analyticity for Multi-Regge Limits of the Bern-Dixon-Smirnov Amplitudes

Richard C. Brower, Horatiu Nastase, Howard J. Schnitzer, Chung-I Tan

备注：: Published version of the paper, which includes an expanded discussion on Steinmann Relation for 5-point function, (sect. 4.3 and footnotes #9 and #10) as well as additional clarifying comments on how this work compares to other recent related works in the concluding section. 74 pages, 17 figures
发表信息：: Nucl.Phys.B822:301-347,2009
DOI：: 10.1016/j.nuclphysb.2009.07.026

英文摘要：

As a consequence of the AdS/CFT correspondence, planar ${\cal N} =4$ super Yang-Mills SU(N) theory is expected to exhibit stringy behavior and multi-Regge asymptotic. In this paper we extend our recent investigation to consider issues of analyticity, a central feature of Regge asymptotics. We contrast flat-space open string theory in the planar limit with the ${\cal N}=4$ super Yang-Mills theory, as represented by the Bern, Dixon and Smirnov \cite{Bern:2005iz} (BDS) conjecture for n-gluon scattering, believed to be exact for $n=4,5$ and modified only by a function of cross-ratios for $n\geq 6$. It is emphasized that multi-Regge factorization should be applied to trajectories with definite signature. A variety of analyticity and factorization constraints realized in flat space string theory are not satisfied by the BDS conjecture, at least when the exponential factors are truncate in the infra-red regulator below $O(ε)$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Implications of multi-Regge limits for the Bern-Dixon-Smirnov conjecture

Planar ${\cal N} =4$ super Yang-Mills SU(N) theory is expected to exhibit stringy behavior, anticipated by the 't Hooft genus expansion and the $AdS/CFT$ correspondence. We examine the Bern-Dixon-Smirnov (BDS) conjecture for $n$-gluon amplitudes in the context of single-Regge and multi-Regge limits and show that these amplitudes have the expected Regge form in the Euclidean region.

2009-02-06hep-phhep-th

BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes

After a brief review of the BFKL approach to Regge processes in QCD and in supersymmetric (SUSY) gauge theories we propose a strategy for calculating the next-to-next-to-leading order corrections to the BFKL kernel. They can be obtained in terms of various cross-sections for Reggeized gluon interactions. The corresponding amplitudes can be calculated in the framework of the effective action for high energy scattering. In the case of N=4 SUSY it is also possible to use the Bern-Dixon-Smirnov (BDS) ansatz. For this purpose the analytic properties of the BDS amplitudes at high energies are invest…

2009-02-09hep-phhep-th

BFKL Pomeron and Bern-Dixon-Smirnov amplitudes in N=4 SUSY

We review the theoretical approaches for investigations of the high energy hadron-hadron scattering in the Regge kinematics. It is demonstrated, that the gluon in QCD is reggeized and the Pomeron is a composite state of the reggeized gluons. Remarkable properties of the BFKL equation for the Pomeron wave function in QCD and supersymmetric gauge theories are outlined. Due to the AdS/CFT correspondence the BFKL Pomeron is equivalent to the reggeized graviton in the extended N=4 SUSY. The properties of the maximal transcendentality and integrability are realized in this model. The BDS multi-gluon…

2008-10-21hep-th

Quark scattering amplitudes at strong coupling

Following Alday and Maldacena, we describe a string theory method to compute the strong coupling behavior of the scattering amplitudes of quarks and gluons in planar N=2 super Yang-Mills theory in the probe approximation. Explicit predictions for these quantities can be constructed using the all-orders planar gluon scattering amplitudes of N=4 super Yang-Mills due to Bern, Dixon and Smirnov.

2007-12-10hep-th

Regge behavior of gluon scattering amplitudes in N=4 SYM theory

It is shown that the four-gluon scattering amplitude for N=4 supersymmetric Yang-Mills theory in the planar limit can be written, in both the weak- and strong-coupling limits, as a reggeized amplitude, with a parent trajectory and an infinite number of daughter trajectories. This result relies crucially on the fact that the leading IR-divergence and the finite log^2(s/t)-dependent piece of the amplitude are characterized by the same function for all values of the coupling, as conjectured by Bern, Dixon, and Smirnov, and proved by Alday and Maldacena in the strong-coupling limit. We use the Ald…

2007-10-31hep-phhep-th

Amplitudes in the beta-deformed Conformal Yang-Mills

We study perturbative amplitudes in a large class of theories obtained by marginal deformations of the N=4 supersymmetric Yang-Mills. We find that planar amplitudes in the deformed theories are closely related to planar amplitudes in the original N=4 SYM. For some classes of deformations the amplitudes essentially coincide with the N=4 amplitudes to all orders in planar perturbation theory. For more general classes of marginal deformations, the equivalence holds at up to four loops, and at five loops it is likely to break down. This implies that the iterative structure of planar MHV amplitudes…

2006-02-08hep-phhep-th

更多相关论文收起更多论文

A Twistor Approach to One-Loop Amplitudes in N=1 Supersymmetric Yang-Mills Theory

We extend the twistor string theory inspired formalism introduced in hep-th/0407214 for calculating loop amplitudes in N=4 super Yang-Mills theory to the case of N=1 (and N=2) super Yang-Mills. Our approach yields a novel representation of the gauge theory amplitudes as dispersion integrals, which are surprisingly simple to evaluate. As an application we calculate one-loop maximally helicity violating (MHV) scattering amplitudes with an arbitrary number of external legs. The result we obtain agrees precisely with the expressions for the N=1 MHV amplitudes derived previously by Bern, Dixon, Dun…

2004-10-28hep-phhep-th

The dimension-shift conjecture for one-loop amplitudes

A conjecture made by Bern, Dixon, Dunbar, and Kosower asserts a simple dimension-shifting relationship between the one-loop structure of N = 4 MHV amplitudes and all-plus helicity amplitudes in pure Yang-Mills theory. We prove this conjecture to all orders in dimensional regularisation using unitarity cuts, and evaluate the form of these simplest one-loop amplitudes using a generalised D-dimensional unitarity technique which captures the full amplitude to all multiplicities.

2021-04-20hep-th

Discretized Minimal Surface and the BDS Conjecture in N=4 Super Yang-Mills Theory at Strong Coupling

We construct numerically the minimal surface in AdS spacetime surrounded by the light-like segments, which are dual to the 4, 6 and 8-point gluon scattering amplitudes in N=4 super Yang-Mills theory. We evaluate the area of the minimal surface in the radial cut-off regularization and compare these areas with the formula conjectured by Bern, Dixon and Smirnov (BDS), which is modified by the remainder function of cross-ratios of external momenta for n(\geq 6)-point amplitudes. In our momentum configuration cross-ratios are constant. We calculate the difference of areas with different conformal b…

2009-04-01hep-th

多雷吉振幅的类KLT构造

A KLT-like construction for multi-Regge amplitudes

受KLT计算步骤启发，将N=4超杨-米尔斯理论多雷吉极限的单值系数散射振幅通过逆梅林变换分解为多值系数振幅的乘积，以六点余函数为例验证了该方法，并指出脱离高度对称弦场景带来的不确定性。

2023-06-28hep-th

QCD 与 $\mathcal{N}=4$ 超杨–米尔斯理论中三圈软定理

Soft Theorem to Three Loops in QCD and ${\cal N} = 4$ Super Yang-Mills Theory

本文利用 Feynman 参数递归积分计算 QCD 两硬部分子过程至三圈的软因子，并借助领先超越性原理得到 $\mathcal{N}=4$ SYM 的全色三圈结果及 BDS 常数解析值。

2024-01-24hep-phhep-th

One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices

We propose a new, twistor string theory inspired formalism to calculate loop amplitudes in N=4 super Yang-Mills theory. In this approach, maximal helicity violating (MHV) tree amplitudes of N=4 super Yang-Mills are used as vertices, using an off-shell prescription introduced by Cachazo, Svrcek and Witten, and combined into effective diagrams that incorporate large numbers of conventional Feynman diagrams. As an example, we apply this formalism to the particular class of MHV one-loop scattering amplitudes with an arbitrary number of external legs in N=4 super Yang-Mills. Remarkably, our approac…

2004-11-27hep-phhep-th

多Regge运动学中的双类空共线极限

Double spacelike collinear limits from multi-Regge kinematics

本研究在平面$\mathcal{N}=4$超杨-米尔斯理论中探究两个胶子对类空共线时的散射振幅与形状因子，发现关联两共线方向的广义分裂振幅符合BDS减六粒子振幅且具有普适性。

2025-07-07hep-th

Reggeization of N=8 Supergravity and N=4 Yang-Mills Theory II

The loop expansion for the n-point functions of N=4 Yang-Mills theory and N=8 supergravity can be formulated as the loop expansion of scalar field theory with an infinite subclass being the ladder diagrams. We consider the sum of ladder diagrams for gluon-gluon and graviton-graviton scattering in the Regge limit. The reggeization of the gluon and the graviton is discussed in this context and that of hep-th/0701217. If the Bern, Dixon, Smirnov conjecture for planar gluon-gluon scattering is correct, then the ladder sum for SU(N) gauge theory at large N, correctly gives the Regge limit, with Reg…

2007-08-17hep-th

Iterated amplitudes in the high-energy limit

We consider the high-energy limits of the colour ordered four-, five- and six-gluon MHV amplitudes of the maximally supersymmetric QCD in the multi-Regge kinematics where all the gluons are strongly ordered in rapidity. We show that various building blocks occurring in the Regge factorisation (the Regge trajectory, the coefficient functions and the Lipatov vertex) satisfy an iterative structure very similar to the Bern-Dixon-Smirnov (BDS) ansatz. This iterative structure, combined with the universality of the building blocks, enables us to show that in the Euclidean region any two- and three-l…

2009-11-10hep-th

Virtual Color-Kinematics Duality: 6-pt 1-Loop MHV Amplitudes

We study 1-loop MHV amplitudes in N=4 super Yang-Mills theory and in N=8 supergravity. For Yang-Mills we find that the simple form for the full amplitude presented by Del Duca, Dixon and Maltoni naturally leads to one that has physical residues on all compact contours. After expanding the simple form in terms of standard scalar integrals, we introduce redundancies under certain symmetry considerations to impose the color-kinematics duality of Bern, Carrasco and Johansson (BCJ). For five particles we directly find the results of Carrasco and Johansson as well as a new compact form for the super…

2013-04-30hep-th