Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory

By J. Drummond, J. Henn, J. Plefka. 2009

523 citations recorded by the source corpus.

Tree-level scattering amplitudes in = 4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a `dual' superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,2|4) of the theory. In this paper we derive the action of the dual superconformal generators in on-shell superspace and extend the dual generators suitably to leave scattering amplitudes invariant. We then study the algebra of standard and dual symmetry generators and show that the inclusion of the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a Yangian. The non-local Yangian generators acting on amplitudes turn out to be cyclically invariant due to special properties of psu(2,2|4). The representation of the Yangian generators takes the same form as in the case of local operators, suggesting that the Yangian symmetry is an intrinsic property of planar = 4 super Yang-Mills, at least at tree level.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7405cbdc4a8da0728698ca7f3fece3d138285146

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Song He
2. S. Caron-Huot
3. Tim Adamo
4. L. Mason
5. F. Cachazo
6. N. Arkani-Hamed
7. C. Cheung
8. A. Sever

In Nuclear and High Energy Physics

1. S. Caron-Huot
2. L. Dixon
3. N. Arkani-Hamed
4. F. Cachazo
5. J. Drummond
6. P. Vieira
7. A. Sever
8. Claude Duhr

Citations in the corpus

• The Grassmannian origin of dual superconformal invariance (2009, background): “Since the full Yangian algebra of N = 4 SYM scattering amplitudes [ 8 ] arises from taking commutators of superconformal and dual superconformal generators, we expect that the object in eq. (1) is invariant under the full Yangian as well.”
• Single-valued harmonic polylogarithms and the multi-Regge limit (2012, background): “Another powerful technique for determining the remainder function is to exploit an infinite-dimensional Yangian invariance [29, 30] which includes the dual superconformal generators.”
• A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon (2014, background): “ve of the remainder function. Including the original superconformal symmetry of the amplitudes, or equivalently invoking parity for the amplitudes, extends dual superconformal symmetry to its Yangian [60, 61], leading to further recursive equations, relevant for determining non-MHV amplitudes. The h”
• Scattering amplitudes and Wilson loops in twistor space (2011, background): “In terms of momentum twistors, the generators of the dual superconformal and standard superconformal are respectively [91]”
• TASI Lectures on Scattering Amplitudes (2017, background): “On-shell tools have excavated a landscape of structures: hidden Yangian and dual conformal symmetries [80, 81, 82, 83, 84], reformulations of the S-matrix in twistor space [85, 86, 22, 87, 88, 89, 90, 91] and Grassmannian space [92, 93, 94], as well as connections to abstract volumes [12, 95] like t”
• Notes on the scattering amplitude — Wilson loop duality (2010, background): “Tree amplitudes in that case have been shown to be invariant under a full dual superconformal [19{23] (in fact Yangian [ 24 ]) while loops carry only a (mildly broken) dual conformal invariance [19, 25] (see also [26]).”
• Loop corrections to soft theorems in gauge theories and gravity (2014, background): “When written in terms of spinor helicity, the operator S (1) YM can be written in a bi-local form very similar to that of Yangian generators for N = 4 SYM [30].”
• Y-system for scattering amplitudes (2010, background): “25 The Yangian charges—responsible for integrability—are also visible at weak coupling [39].”
• Scattering Amplitudes and the Positive Grassmannian (2012, background): “In this section, we illustrate the remarkable fact that the leading generators of infinitesimal positive diffeomorphisms directly match the level-one generators of the Yangian as described in [111] (see also [110,112,113]).”
• The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM (2010, background): “It was quickly realized that the BCFW form of the tree amplitudes manifested both full superconformal and dual superconformal invariance, which together close into an infinite-dimensional Yangian symmetry algebra [28].”
• Symmetries of Tree-level Scattering Amplitudes in N = 6 Superconformal Chern{Simons Theory (2010, methodology): “Even without a dual symmetry, however, a procedure to consistently promote certain standard Lie algebra representations to Yangian representations is wellknown [24, 25, 17].”
• Dual superconformal invariance, momentum twistors and Grassmannians (2009, background): “ momentum space’ (differences between two region momenta are the momenta of the particles in the scattering process), as opposed to ordinary Minkowski space. It is a hidden symmetry that may be viewed [2] as part of the Yangian structure of N = 4 SYM [3] predicted by AdS/CFT [4]. The MHV and six part”