One-Loop N = 4 Super Yang-Mills Scattering Amplitudes to All Orders in the Dimensional Regularization Parameter

Abstract

In this paper we discuss in detail computational methods and new results for one-loop virtual corrections to N = 4 super Yang-Mills scattering amplitudes calculated to all orders in epsilon, the dimensional regularization parameter. 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 small epsilon limit. 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 will 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. To make the presentation as self-contained as possible, we extensively review the prerequisites necessary to understand the main results of this work.

134 pages, 18 figures. "The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory" (arXiv:1009.1376) by Kosower et. al. refers to this work (ref. 25); in v2: added refs. and updated A.2; in v3: fixed Fig. 1 and eq. (2.7); in v4: incorporated referee suggestions in text (see arXiv:1104.3873), added refs., and fixed eqs. (6.41) and (6.42); in v5: fixed eq. (2.23) and Fig. 12

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• New Relations for Gauge-Theory Amplitudes
• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• Direct extraction of one-loop integral coefficients
• Full one-loop amplitudes from tree amplitudes
• D-dimensional unitarity cut method
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• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
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• From Twistor Actions to MHV Diagrams
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• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• Amplitude for N-Gluon Superstring Scattering
• Iterated amplitudes in the high-energy limit
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Cited by in corpus (5)

• An Introduction to On-shell Recursion Relations
• The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
• Symbols of One-Loop Integrals From Mixed Tate Motives
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes