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

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.

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

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• Scattering Amplitudes
• The Structure of n-Point One-Loop Open Superstring Amplitudes
• Scattering amplitudes: the most perfect microscopic structures in the universe
• An Introduction to On-shell Recursion Relations
• The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
• WiLE: a Mathematica package for weak coupling expansion of Wilson loops in ABJ(M) theory
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes