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Register a new userA tale of two Regge limits
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Authors
Vittorio Del Duca
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In light of the strong advances in understanding the mathematical structure of scattering amplitudes, we discuss the Regge limit of QCD and of the ${cal N}=4$ Super Yang-Mills theory.
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Pure Yang-Mills amplitudes with all external gluons carrying positive helicity, known as all-plus amplitudes, have an especially simple structure. The tree amplitudes vanish and, up to at least two loops, the loop-level amplitudes are related to those of $mathcal{N}=4$ super-Yang-Mills (SYM) theory. This makes all-plus amplitudes a useful testing ground for new methods of simplifying more general classes of amplitudes. In this thesis we consider three new approaches, focusing on the structure before integration.
We introduce a method to extract the symbol of the coefficient of $(2pi i)^2$ of MHV remainder functions in planar N=4 Super Yang-Mills in multi-Regge kinematics region directly from the symbol in full kinematics. At two loops this symbol can be uplifted to the full function in a unique way, without any beyond-the-symbol ambiguities. We can therefore determine all two-loop MHV amplitudes at function level in all kinematic regions with different energy signs in multi-Regge kinematics. We analyse our results and we observe that they are consistent with the hypothesis of a contribution from the exchange of a three-Reggeon composite state starting from two loops and eight points in certain kinematic regions.
We calculate the mass of the lowest lying spin two glueball in N=1 super Yang-Mills from the dual Klebanov-Strassler background. We show that the Regge trajectory obtained is linear; the 0++, 1-- and 2++ states lie on a line of slope 0.23 -measured in units of the conifold deformation. We also compare mass ratios with lattice data and find agreement within one standard deviation.
The structure constants of twist-two operators with spin $j$ in the BFKL limit $g^2rightarrow 0, jrightarrow 1$ but ${g^2over j-1}sim 1$ are determined from the calculation of the three-point correlator of twist-two light-ray operators in the triple Regge limit. It is well known that the anomalous dimensions of twist-two operators in this limit are determined by the BFKL intercept. Similarly, the obtained structure constants are determined by an analytic function of three BFKL intercepts.
Wilson lines capture important features of scattering amplitudes, for example soft effects relevant for infrared divergences, and the Regge limit. Beyond the leading power approximation, corrections to the eikonal picture have to be taken into account. In this paper, we study such corrections in a model of massive scattering amplitudes in N = 4 super Yang-Mills, in the planar limit, where the mass is generated through a Higgs mechanism. Using known three-loop analytic expressions for the scattering amplitude, we find that the first power suppressed term has a very simple form, equal to a single power law. We propose that its exponent is governed by the anomalous dimension of a Wilson loop with a scalar inserted at the cusp, and we provide perturbative evidence for this proposal. We also analyze other limits of the amplitude and conjecture an exact formula for a total cross-section at high energies.
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