A super MHV vertex expansion for N=4 SYM theory

作者：Kiermaier Michael^*; Naculich Stephen G

来源：The Journal of High Energy Physics, 2009, 2009(5): 072.

DOI：10.1088/1126-6708/2009/05/072

• Supersymmetric gauge theory
• Extended Supersymmetry

We present a supersymmetric generalization of the MHV vertex expansion for all tree amplitudes in N = 4 SYM theory. In addition to the choice of a reference spinor, this super MHV vertex expansion also depends on four reference Grassmann parameters. We demonstrate that a significant fraction of diagrams in the expansion vanishes for a judicious choice of these Grassmann parameters, which simplifies the computation of amplitudes. Even pure-gluon amplitudes require fewer diagrams than in the ordinary MHV vertex expansion.
We show that the super MHV vertex expansion arises from the recursion relation associated with a holomorphic all-line supershift. This is a supersymmetric generalization of the holomorphic all-line shift recently introduced in arXiv:0811.3624. We study the large-z behavior of generating functions under these all-line supershifts, and find that they generically provide 1/z(k) falloff at (Next-to)(MHV)-M-k level. In the case of anti-MHV generating functions, we find that a careful choice of shift parameters guarantees a stronger 1/z(k 4) falloff. These particular all-line supershifts may therefore play an important role in extending the super MHV vertex expansion to N = 8 supergravity.

• 出版日期2009-5