Logarithmic singularities and maximally supersymmetric amplitudes

@article{Bern2014LogarithmicSA,
  title={Logarithmic singularities and maximally supersymmetric amplitudes},
  author={Zvi Bern and Enrico Herrmann and Sean Litsey and James Stankowicz and Jaroslav Trnka},
  journal={Journal of High Energy Physics},
  year={2014},
  volume={2015},
  pages={1-70}
}
A bstractThe dual formulation of planar N=4$$ \mathcal{N}=4 $$ super-Yang-Mills scattering amplitudes makes manifest that the integrand has only logarithmic singularities and no poles at infinity. Recently, Arkani-Hamed, Bourjaily, Cachazo and Trnka conjectured the same singularity properties hold to all loop orders in the nonplanar sector as well. Here we conjecture that to all loop orders these constraints give us the key integrand level analytic information contained in dual conformal… 

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References

SHOWING 1-10 OF 124 REFERENCES

Unification of residues and Grassmannian dualities

The conjectured duality relating all-loop leading singularities of n-particle Nk−2MHV scattering amplitudes in $$ \mathcal{N} = 4 $$ SYM to a simple contour integral over the Grassmannian G(k, n)

Spectral parameters for scattering amplitudes in $ \mathcal{N} $ =4 super Yang-Mills theory

A bstractPlanar $ \mathcal{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

The Grassmannian origin of dual superconformal invariance

A dual formulation of the S Matrix for $$ \mathcal {N} $$ = 4 SYM has recently been presented, where all leading singularities of n-particle Nk−2MHV amplitudes are given as an integral over the

Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops

We present an Ansatz for the planar five-loop four-point amplitude in maximally supersymmetric Yang-Mills theory in terms of loop integrals. This Ansatz exploits the recently observed correspondence

Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes

We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N = 4 super-Yang-Mills theory, including the nonplanar contributions.

Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond

We compute the leading-color (planar) three-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4 - 2{epsilon} dimensions, as a Laurent expansion about {epsilon} = 0 including the

Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N = 8 Supergravity

Using the method of maximal cuts, we obtain a form of the three-loop four-point scattering amplitude of $\mathcal{N}=8$ supergravity in which all ultraviolet cancellations are made manifest. The

The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM

We give an explicit recursive formula for the all ℓ-loop integrand for scattering amplitudes in $ \mathcal{N} = 4 $ SYM in the planar limit, manifesting the full Yangian symmetry of the theory. This

The soft-collinear bootstrap: $ \mathcal{N} = {4} $ Yang-Mills amplitudes at six- and seven-loops

A bstractInfrared divergences in scattering amplitudes arise when a loop momentum ℓ becomes collinear with a massless external momentum p. In gauge theories, it is known that the L-loop logarithm of

Local spacetime physics from the Grassmannian

A duality has recently been conjectured between all leading singularities of n-particle Nk−2MHV scattering amplitudes in $ \mathcal{N} = 4 $ SYM and the residues of a contour integral with a natural
...