University of Hertfordshire
http://hdl.handle.net/2299/6050
For Pure Research Information System connection2018-10-21T12:27:56ZN=4 Scattering Amplitudes and the Deformed Grassmannian
http://hdl.handle.net/2299/20732
N=4 Scattering Amplitudes and the Deformed Grassmannian
Ferro, Livia; Lukowski, Tomasz; Staudacher, Matthias
Some time ago the general tree-level scattering amplitudes of N=4 Super Yang-Mills theory were expressed as certain Grassmannian contour integrals. These remarkable formulas allow to clearly expose the super-conformal, dual super-conformal, and Yangian symmetries of the amplitudes. Using ideas from integrability it was recently shown that the building blocks of the amplitudes permit a natural multi-parameter deformation. However, this approach had been criticized by the observation that it seemed impossible to reassemble the building blocks into Yangian-invariant deformed non-MHV amplitudes. In this note we demonstrate that the deformations may be succinctly summarized by a simple modification of the measure of the Grassmannian integrals, leading to a Yangian-invariant deformation of the general tree-level amplitudes. Interestingly, the deformed building-blocks appear as residues of poles in the spectral parameter planes. Given that the contour integrals also contain information on the amplitudes at loop-level, we expect the deformations to be useful there as well. In particular, applying meromorphicity arguments, they may be expected to regulate all notorious infrared divergences. We also point out relations to Gelfand hypergeometric functions and the quantum Knizhnik-Zamolodchikov equations.
15 pages
2014-12-01T00:00:00ZSpectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
http://hdl.handle.net/2299/20731
Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
Ferro, Livia; Lukowski, Tomasz; Meneghelli, Carlo; Plefka, Jan; Staudacher, Matthias
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.
49 pages, 20 figures; v2: typos fixed
2014-01-17T00:00:00ZLessons from crossing symmetry at large N
http://hdl.handle.net/2299/20730
Lessons from crossing symmetry at large N
Alday, Luis F.; Bissi, Agnese; Lukowski, Tomasz
We consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale \Delta_{gap} and are consistent with the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. These solutions organize as a double expansion in 1/c and 1/\Delta_{gap}. Our solutions are valid to leading order in 1/c and to all orders in 1/\Delta_{gap} and reproduce, in particular, instanton corrections previously found. Furthermore, we find a connection between such upper bounds and positivity constraints arising from causality in flat space. Finally, we show that certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.
20 pages, v2: Assumptions stated more clearly, version published in JHEP
2015-06-12T00:00:00ZA Shortcut to General Tree-level Scattering Amplitudes in N=4 SYM via Integrability
http://hdl.handle.net/2299/20729
A Shortcut to General Tree-level Scattering Amplitudes in N=4 SYM via Integrability
Kanning, Nils; Lukowski, Tomasz; Staudacher, Matthias
We combine recent applications of the two-dimensional quantum inverse scattering method to the scattering amplitude problem in four-dimensional N=4 Super Yang-Mills theory. Integrability allows us to obtain a general, explicit method for the derivation of the Yangian invariants relevant for tree-level scattering amplitudes in the N=4 model.
18 pages, 7 figures; v2: minor changes, references added. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
2014-03-13T00:00:00Z