Gravity on-shell diagrams

Trnka

2019

Self Cite

In this work we explore the properties of four-dimensional gravity integrands at large loop momenta. This analysis can not be done directly for the full offshell integrand but only becomes well-defined on cuts that allow us to unambiguously specify labels for the loop variables. The ultraviolet region of scattering amplitudes originates from poles at infinity of the loop integrands and we show that in gravity these integcrands conceal a number of surprising features. In particular, certain poles at infinity are absent which requires a conspiracy between individual Feynman integrals contributing to the amplitude. We suspect that this non-trivial behavior is a consequence of yet-to-be found symmetry or hidden property of gravity amplitudes. We discuss mainly amplitudes in N = 8 supergravity but most of the statements are valid for pure gravity as well.

mentioning

confidence: 75%

UV cancellations in gravity loop integrands

Trnka

2019

Self Cite

“…Even though they have been most prominently featured in the realm of supersymmetric theories [21,[129][130][131][132][133] (see e.g. [134,135] for some exceptions), they can generally be defined from first principles without reference to (off-shell) loop integrands in any quantum field theory.…”

Section: Jhep06(2017)059mentioning

confidence: 99%

Prescriptive unitarity

Bourjaily

Trnka

2017

Self Cite

116

We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in the case of planar, maximally supersymmetric Yang-Mills theory (SYM), where we construct closed-form representations of all (n-point N k MHV) scattering amplitudes through three loops. The prescriptive approach contrasts with the ordinary description of unitarity-based methods by avoiding any need for linear algebra to determine integrand coefficients. We describe this approach in general terms as it should have applications to many quantum field theories, including those without planarity, supersymmetry, or massless spectra defined in any number of dimensions.

“…There does not yet exist any truly satisfactory approach to the computation of general on-shell functions in SUGRA. Although (as with all massless quantum field theories in four dimensions) there exists suggestive representations of on-shell functions in terms of Grassmannian integrals [94], the actual expressions found for leading singularities in SUGRA still surprise us with their simplicity.…”

Section: B2 Two-loop Leading Singularities Of Mhv Amplitudes In Sugramentioning

confidence: 99%

Prescriptive unitarity for non-planar six-particle amplitudes at two loops

Bourjaily

Langer

et al. 2019

Self Cite

We extend the applications of prescriptive unitarity beyond the planar limit to provide local, polylogarithmic, integrand-level representations of six-particle MHV scattering amplitudes in both maximally supersymmetric Yang-Mills theory and gravity. The integrand basis we construct is diagonalized on a spanning set of non-vanishing leading singularities that ensures the manifest matching of all softcollinear singularities in both theories. As a consequence, this integrand basis naturally splits into infrared-finite and infrared-divergent parts, with hints toward an integrand-level exponentiation of infrared divergences. Importantly, we use the same basis of integrands for both theories, so that the presence or absence of residues at infinite loop momentum becomes a feature detectable by inspecting the cuts of the theory. Complete details of our results are provided as ancillary files to this work's submission to the arXiv. arXiv:1909.09131v1 [hep-th]