Ruth Britto

Direct Proof of the Tree-Level Scattering Amplitude Recursion Relation in Yang-Mills Theory

Recently, by using the known structure of one-loop scattering amplitudes for gluons in Yang-Mills theory, a recursion relation for tree-level scattering amplitudes has been deduced. Here, we give a short and direct proof of this recursion relation based on properties of tree-level amplitudes only.

New recursion relations for tree amplitudes of gluons

Abstract We present new recursion relations for tree amplitudes in gauge theory that give very compact formulas. Our relations give any tree amplitude as a sum over terms constructed from products of two amplitudes of fewer particles multiplied by a Feynman propagator. The two amplitudes in each term are physical, in the sense that all particles are on-shell and momentum conservation is preserved. This is striking, since it is just like adding certain factorization limits of the original amplitude to build up the full answer. As examples, we recompute all known tree-level amplitudes of up to seven gluons and show that our recursion relations naturally give their most compact forms. We give a new result for an eight-gluon amplitude, A ( 1 + , 2 − , 3 + , 4 − , 5 + , 6 − , 7 + , 8 − ) . We show how to build any amplitude in terms of three-gluon amplitudes only.

Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills

Abstract One-loop amplitudes of gluons in N = 4 gauge theory can be written as linear combinations of known scalar box integrals with coefficients that are rational functions. In this paper we show how to use generalized unitarity to basically read off the coefficients. The generalized unitarity cuts we use are quadruple cuts. These can be directly applied to the computation of four-mass scalar integral coefficients, and we explicitly present results in next-to-next-to-MHV amplitudes. For scalar box functions with at least one massless external leg we show that by doing the computation in signature ( − − + + ) the coefficients can also be obtained from quadruple cuts, which are not useful in Minkowski signature. As examples, we reproduce the coefficients of some one-, two-, and three-mass scalar box integrals of the seven-gluon next-to-MHV amplitude, and we compute several classes of three-mass and two-mass-hard coefficients of next-to-MHV amplitudes to all multiplicities.

One-loop amplitudes of gluons in supersymmetric QCD

One-loop amplitudes of gluons in supersymmetric Yang-Mills are four-dimensional cut-constructible. This means that they can be determined from their unitarity cuts. We present a new systematic procedure to explicitly carry out any finite unitarity cut integral. The procedure naturally separates the contributions from bubble, triangle and box scalar integrals. This technique allows the systematic calculation of

Computing one-loop amplitudes from the holomorphic anomaly of unitarity cuts

mathcal{N}=1

Deformed superspace, N = 1/2 supersymmetry and nonrenormalization theorems

amplitudes of gluons. As an application we compute all next-to-MHV six-gluon amplitudes in

N=1/2 Wess-Zumino model is renormalizable.

mathcal{N}=1

Non(anti)commutative superspace, UV/IR mixing & open Wilson lines

super-Yang-Mills.

All split helicity tree-level gluon amplitudes

We propose a systematic way to carry out the method introduced in F. Cachazo, hep-th/0410077 for computing certain unitarity cuts of one-loop N=4 amplitudes of gluons. We observe that the class of cuts for which the method works involves all next-to-MHV n-gluon one-loop amplitudes of any helicity configurations. As an application of our systematic procedure, we obtain the complete seven-gluon one-loop leading-color amplitude A{sub 7;1}(1{sup -},2{sup -},3{sup -},4{sup +},5{sup +},6{sup +},7{sup +})

Deformed superspace, = 1/2 supersymmetry & (non)renormalization theorems

We consider a deformed superspace in which the coordinates θ do not anticommute, but satisfy a Clifford algebra. We present results on the properties of = 1/2 supersymmetric theories of chiral superfields in deformed superspace, taking the Wess-Zumino model as the prototype. We prove new (non)renormalization theorems: the F-term is radiatively corrected and becomes indistinguishable from the D-term, while the -term is not renormalized. Supersymmetric vacua are critical points of the antiholomorphic superpotential. The vacuum energy is zero to all orders in perturbation theory. We illustrate these results with several examples.