On tree amplitudes in gauge theory and gravity

By N. Arkani-Hamed, Jared Kaplan. 2008

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The BCFW recursion relations provide a powerful way to compute tree amplitudes in gauge theories and gravity, but only hold if some amplitudes vanish when two of the momenta are taken to infinity in a particular complex direction. This is a very surprising property, since individual Feynman diagrams all diverge at infinite momentum. In this paper we give a simple physical understanding of amplitudes in this limit, which corresponds to a hard particle with (complex) light-like momentum moving in a soft background, and can be conveniently studied using the background field method exploiting background light-cone gauge. An important role is played by enhanced spin symmetries at infinite momentum-a single copy of a ``Lorentz group for gauge theory and two copies for gravity-which together with Ward identities give a systematic expansion for amplitudes at large momentum. We use this to study tree amplitudes in a wide variety of theories, and in particular demonstrate that certain pure gauge and gravity amplitudes do vanish at infinity. Thus the BCFW recursion relations can be used to compute completely general gluon and graviton tree amplitudes in any number of dimensions. We briefly comment on the implications of these results for computing massive 4D amplitudes by KK reduction, as well understanding the unexpected cancelations that have recently been found in loop-level gravity amplitudes.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4a685225cf7e5edb46c5e3b42c584d6e6a8df8ca

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Citations in the corpus

Black Hole Formation and Classicalization in Ultra-Planckian 2 ! N Scattering (2014, background): “ction 5 in this Eikonal limit the gauge and gravitational superstring amplitudes assume a form which is suited to study properties known from eld{theory amplitudes in the large complex momentum limit [19]. The latter gives a relation between BCFW relations and the pomeron vertex in string theory [20”
Analyticity and the holographic S-matrix (2011, methodology): “The remarkably simple properties of the scattering amplitudes themselves [43, 44, 45, 46, 47, 48, 41, 42] and the existence of matrix models [49] might be viewed as evidence for this sort of conjecture.”
Taming tree amplitudes in general relativity (2007, background): “Luckily, a proof that equal helicity gravitons can also be defomed was recently given by ArkaniHamed and Kaplan in [42].”
Factorization properties of soft graviton amplitudes (2011, background): “ alternatives. A third reason for studying gravity is that there are intriguing connections between the structure of perturbative scattering amplitudes in gravity and non-abelian gauge theories (e.g. [2, 3, 4, 5, 6, 7]). A possible application of these ideas is, for example, that of settling the que”
On the tensionless limit of string theory, off-shell higher spin interaction vertices and BCFW recursion relations (2010, methodology): “Alternatively one could use the method of [54].”
A natural language for AdS/CFT correlators (2011, methodology): “To efficiently compute these amplitudes in Mellin space, we would require some version of the BCFW recursion relations [45, 46, 47] analogous to the one developed in momentum space for AdS [48, 49].”
Proof of the formula of Cachazo, He and Yuan for Yang-Mills tree amplitudes in arbitrary dimension (2013, background): “The residues of these poles are given by the product of amplitudes Am, where m < N and so A φ N (ζ) can be expressed as a sum over these residues, and this provides a recursion relation, which is the BCFW relation [4, 7].”
Zoology of condensed matter: framids, ordinary stuff, extra-ordinary stuff (2015, background): “Interestingly, a similar enhanced “spin” symmetry applies to gauge-theory amplitudes in certain infinitemomentum limits [31].”
One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts (2011, methodology): “Following [105], it is convenient to choose a reference frame where the momentum of the gluon g1 is p1 = μ(1,0⊥, 1) and the momentum of the gluon gj is pj = μ(1,0⊥,−1), where μ is a constant with the mass dimension one.”
TASI Lectures on Scattering Amplitudes (2017, background): “Remarkably, the boundary term B∞ vanishes both in gauge theory and gravity as long as the momentum shift is applied to external legs with the appropriate configuration of helicities [44, 49].”
Generating tree amplitudes in Script N = 4 SYM and Script N = 8 SG (2008, methodology): “Perhaps the method of [27] can be generalized to 3-line shifts and applied for this purpose.”
The Cosmological Optical Theorem (2020, background): “In fact, one of the greatest achievements of the amplitude program is the on-shell construction of all tree level amplitudes of YM and GR [48, 49, 50, 51, 52].”
A brief introduction to modern amplitude methods (2013, unknown): “However, it is possible to show [26] using the background field method that the [+,+〉 and [−,−〉 cases are actually just as well behaved as the [−,+〉 case, also falling off like 1/z.”