TY - JOUR

T1 - Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory

AU - Ferro, Livia

AU - Lukowski, Tomasz

AU - Meneghelli, Carlo

AU - Plefka, Jan

AU - Staudacher, Matthias

N1 - 49 pages, 20 figures; v2: typos fixed

PY - 2014/1/17

Y1 - 2014/1/17

N2 - Planar N=4 Super Yang-Mills theory appears to be a quantum integrable four-dimensional conformal theory. This has been used to find equations believed to describe its exact spectrum of anomalous dimensions. Integrability seemingly also extends to the planar space-time scattering amplitudes of the N=4 model, which show strong signs of Yangian invariance. However, in contradistinction to the spectral problem, this has not yet led to equations determining the exact amplitudes. We propose that the missing element is the spectral parameter, ubiquitous in integrable models. We show that it may indeed be included into recent on-shell approaches to scattering amplitude integrands, providing a natural deformation of the latter. Under some constraints, Yangian symmetry is preserved. Finally we speculate that the spectral parameter might also be the regulator of choice for controlling the infrared divergences appearing when integrating the integrands in exactly four dimensions.

AB - Planar N=4 Super Yang-Mills theory appears to be a quantum integrable four-dimensional conformal theory. This has been used to find equations believed to describe its exact spectrum of anomalous dimensions. Integrability seemingly also extends to the planar space-time scattering amplitudes of the N=4 model, which show strong signs of Yangian invariance. However, in contradistinction to the spectral problem, this has not yet led to equations determining the exact amplitudes. We propose that the missing element is the spectral parameter, ubiquitous in integrable models. We show that it may indeed be included into recent on-shell approaches to scattering amplitude integrands, providing a natural deformation of the latter. Under some constraints, Yangian symmetry is preserved. Finally we speculate that the spectral parameter might also be the regulator of choice for controlling the infrared divergences appearing when integrating the integrands in exactly four dimensions.

KW - hep-th

U2 - 10.1007/JHEP01(2014)094

DO - 10.1007/JHEP01(2014)094

M3 - Article

VL - 2014

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

M1 - 94

ER -