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

摘要

In this review, we discuss some recent developments related to one-loop N = 4 super-YangMills scattering amplitudes calculated to all orders in ε. It is often the case that one-loop gauge theory computations are carried out to O(ε ~0), since higher order in ε contributions vanish in the ε → 0 limit. We will show, however, that the higher order contributions are actually quite useful. In the context of maximally supersymmetric YangMills, 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-ε one-loop N = 4 super-YangMills amplitudes and the first and second stringy corrections to analogous treelevel superstring amplitudes. For our second example, we will derive a new result for the all-orders-in-ε 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.