A current algebra for some gauge theory amplitudes

Abstract

The classical amplitude for scattering of two positive helicity and n-2 negative helicity (or the other way) gauge bosons is shown to be generated by a Wess-Zumino-Witten (WZW) model for N= 4 supersymmetric gauge theory; i.e. the current algebra of the WZW model (with central charge k= 1 ) gives a Kac-Moody algebra as the symmetry behind these amplitudes.

One-Loop Maximal Helicity Violating Amplitudes in N=4 Super Yang-Mills Theories

“…The amplitudes with two negative helicity are called maximally helicity violating (MHV) amplitudes. For N = 4 SYM theories, a MHV amplitude is given by the generalized Parke-Taylor formula which includes particles of all helicity [25]:…”

MHV-vertices for gravity amplitudes

“…Given the assumption that gravity amplitudes are sufficiently well behaved under a BCFW-style analytic continuation to complex momenta, we have presented a direct proof of the formalism and have illustrated its usefulness through concrete examples such as NMHV amplitudes. Although we have presented MHV-vertices for external gravitons only we expect the procedure to extend to other matter types using supersymmetry to obtain the relevant MHV-vertex [6,39]. Although the existence of the CSW formalism can be motivated by the duality with a twistor string theory, such a motivation is not so clear for gravity.…”

“…Inspired by the duality between twistor string theory and Yang-Mills [5] (and generalising a previous description of the simplest gauge theory amplitudes by Nair [6]), Cachazo, Svrček and Witten proposed a reformulation of perturbation theory in terms of off-shell MHV-vertices [7], which can be depicted,…”

“…[22] it was demonstrated that such shifts exist and can be used to derive the MHV vertex approach in gauge theory. The shift affects all of the negative helicity legs, k m i ,λ 6) with the r i chosen to ensure momentum conservation. Most of the above developments have been made for gauge theory amplitudes.…”

On supertwistors, the Penrose--Ward transform and $\CN=4$ super-Yang--Mills theory

“…For more details on the Kleinian case ε = +1, see Appendix C. To smoothen the discussion in the following, we ignore this subtlety and use always (2.20) implying the restriction to the spaceP 3 in all necessary cases. Furthermore, we will call matrix-valued functions τ ε -regular, if they are regular 11 for all values of λ ∈ D in the case ε = −1 and regular for λ ∈ D with |λ| = 1 in the case ε = +1 (and also for the real structure τ 0 ), where D ⊆ CP 1 is the domain under consideration.…”