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      One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops

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          Abstract

          In this review we discuss some recent developments related to one-loop N = 4 super Yang-Mills scattering amplitudes calculated to all orders in epsilon. It is often the case that one-loop gauge theory computations are carried out to order epsilon^0, since higher order in epsilon contributions vanish in the limit as epsilon goes to zero. We will show, however, that the higher order contributions are actually quite useful. In the context of maximally supersymmetric Yang-Mills, we consider two examples in detail to illustrate our point. First we concentrate on computations with gluonic external states and argue that N = 4 supersymmetry implies a simple relation between all-orders-in-epsilon one-loop N = 4 super Yang-Mills amplitudes and the first and second stringy corrections to analogous tree-level superstring amplitudes. For our second example we will derive a new result for the all-orders-in-epsilon one-loop superamplitude for planar six-particle NMHV scattering, an object which allows one to easily obtain six-point NMHV amplitudes with arbitrary external states. We will then discuss the relevance of this computation to the evaluation of the ratio of the planar two-loop six-point NMHV superamplitude to the planar two-loop six-point MHV superamplitude, a quantity which is expected to have remarkable properties and has been the subject of much recent investigation.

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          Amplitude forn-Gluon Scattering

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            DIRAC-BORN-INFELD ACTION FROM DIRICHLET σ-MODEL

            R.G. LEIGH (1989)
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              Perturbative Gauge Theory As A String Theory In Twistor Space

              Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of \({\cal N}=4\) super Yang-Mills theory and the \(D\)-instanton expansion of a certain string theory, namely the topological \(B\) model whose target space is the Calabi-Yau supermanifold \(\Bbb{CP}^{3|4}\).
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                Author and article information

                Journal
                19 April 2011
                2015-01-10
                Article
                10.1088/1751-8113/44/45/454007
                1104.3873
                ef7a89f4-1372-45b3-8dd9-5927b4035736

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                IFT-UAM/CSIC-11-22
                72 pages, 4 figures. Invited review to appear in "Scattering Amplitudes in Gauge Theories," special issue of Journal of Physics A, R. Roiban (ed), M. Spradlin (ed), A. Volovich (ed); v3 matches the final, published version of this article apart from a missing equation number (90). Please note the change of title
                hep-th

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