Tropicalized massive scalar QFT is exactly solvable via a non-linear recursion for effective action coefficients that computes graph moduli space volumes, enabling a polynomial-time sampling algorithm for high-order perturbative contributions.
The All-Loop Integrand For Scattering Amplitudes in PlanarN=4SYM
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
abstract
We give an explicit recursive formula for the all L-loop integrand for scattering amplitudes in N=4 SYM in the planar limit, manifesting the full Yangian symmetry of the theory. This generalizes the BCFW recursion relation for tree amplitudes to all loop orders, and extends the Grassmannian duality for leading singularities to the full amplitude. It also provides a new physical picture for the meaning of loops, associated with canonical operations for removing particles in a Yangian-invariant way. Loop amplitudes arise from the "entangled" removal of pairs of particles, and are naturally presented as an integral over lines in momentum-twistor space. As expected from manifest Yangian-invariance, the integrand is given as a sum over non-local terms, rather than the familiar decomposition in terms of local scalar integrals with rational coefficients. Knowing the integrands explicitly, it is straightforward to express them in local forms if desired; this turns out to be done most naturally using a novel basis of chiral, tensor integrals written in momentum-twistor space, each of which has unit leading singularities. As simple illustrative examples, we present a number of new multi-loop results written in local form, including the 6- and 7-point 2-loop NMHV amplitudes. Very concise expressions are presented for all 2-loop MHV amplitudes, as well as the 5-point 3-loop MHV amplitude. The structure of the loop integrand strongly suggests that the integrals yielding the physical amplitudes are "simple", and determined by IR-anomalies. We briefly comment on extending these ideas to more general planar theories.
citation-role summary
background 1
citation-polarity summary
verdicts
UNVERDICTED 4roles
background 1polarities
background 1representative citing papers
First numerical evaluation of planar two-loop helicity amplitudes for W-boson plus four partons using finite-field reduction and sector decomposition on a subset of master integrals.
A new Mathematica package computes tree amplitudes with arbitrary gauge bosons and arbitrarily charged massless fermions by reducing distinct-flavor partial amplitudes to linear combinations of single-flavor supersymmetric Yang-Mills components.
Adapts BCFW-style recursion to deformed ABHY-associahedron and D-type cluster polytopes for tree-level and one-loop amplitudes in multi-scalar cubic theories.
citing papers explorer
-
Tropicalized quantum field theory and global tropical sampling
Tropicalized massive scalar QFT is exactly solvable via a non-linear recursion for effective action coefficients that computes graph moduli space volumes, enabling a polynomial-time sampling algorithm for high-order perturbative contributions.
-
A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons
First numerical evaluation of planar two-loop helicity amplitudes for W-boson plus four partons using finite-field reduction and sector decomposition on a subset of master integrals.
-
Tree Amplitudes with Charged Matter in Pure Gauge Theory
A new Mathematica package computes tree amplitudes with arbitrary gauge bosons and arbitrarily charged massless fermions by reducing distinct-flavor partial amplitudes to linear combinations of single-flavor supersymmetric Yang-Mills components.
-
BCFW like recursion for Deformed Associahedron
Adapts BCFW-style recursion to deformed ABHY-associahedron and D-type cluster polytopes for tree-level and one-loop amplitudes in multi-scalar cubic theories.