Heptagon amplitude in the multi-Regge regime

J Bartels,V Schomerus,M Sprenger

doi:10.1007/jhep10(2014)067

J Bartels, V Schomerus + Show 1 more

Open Access

https://doi.org/10.1007/jhep10(2014)067

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Abstract

As we have shown in previous work, the high energy limit of scattering amplitudes in N=4 supersymmetric Yang-Mills theory corresponds to the infrared limit of the 1-dimensional quantum integrable system that solves minimal area problems in AdS5. This insight can be developed into a systematic algorithm to compute the strong coupling limit of amplitudes in the multi-Regge regime through the solution of auxiliary Bethe Ansatz equations. We apply this procedure to compute the scattering amplitude for n=7 external gluons in different multi-Regge regions at infinite 't Hooft coupling. Our formulas are remarkably consistent with the expected form of 7-gluon Regge cut contributions in perturbative gauge theory. A full description of the general algorithm and a derivation of results will be given in a forthcoming paper.

Highlights

This minimal area problem was shown to possess an intriguing reformulation in which the area is reproduced by the free energy of a 1-dimensional quantum integrable system [8, 9]
As we have shown in previous work, the high energy limit of scattering amplitudes in N = 4 supersymmetric Yang-Mills theory at strong coupling corresponds to the infrared limit of the 1-dimensional quantum integrable system that solves minimal area problems in AdS5
As we briefly reviewed in the introduction, in strongly coupled N = 4 SYM theory scattering may be reformulated as a minimal area problem

Summary

Kinematics

In this article we consider 2 → n − 2 production amplitudes for massless external gluons. In the multi-Regge limit, the cross ratios u1σ tend to u1σ ∼ 1 while the remaining ones tend to zero, i.e. u2σ, u3σ ∼ 0. Cross ratios with the same index σ approach their limiting values such that the following reduced cross ratios remain finite u2σ 1 − u1σ. Through these equations we have introduced the n − 5 complex parameters wσ. We choose to continue the 6 basic cross ratios along the following curves Pν1ν2ν3 : P−−+ : u11(φ) = e−2iφu , u21(φ) = u21 , u31(φ) = u31 , u12(φ) = u12 , u22(φ) = e−iφu , u32(φ) = eiφu32 ,. These paths and their construction will be discussed in much more detail in our upcoming publication [10]

Weak coupling

Strong coupling

Conclusion and outlook