Cluster algebras for Feynman integrals (Remote talk)

par Dmitry Chicherin (LAPTh)

jeudi 27 mai 2021, 11:00 → 12:00 Europe/Paris

Calculation of the loop Feynman integrals and scattering amplitudes is
considerably facilitated once the relevant space of transcendental
functions is identified. A lot of physically interesting processes can
be expressed in terms of the generalized polylogarithmic functions, and
moreover, a finite-dimensional subspace (at each given loop order) of
the generalized polylogarithms is sufficient in many cases. The latter
is encoded by a finite collection of polynomials (called the alphabet)
in kinematic variables, which represent Landau singularities of the
Feynman integrals and loop amplitudes. Unraveling a hidden mathematical
structure in the alphabet is of great relevance. It has been known for a
while that the alphabets of six- and seven-particle scattering
amplitudes in maximally supersymmetric Yang-Mills theory are cluster
coordinates of A3 and E6 finite cluster algebras, respectively. We will
show that the cluster algebra description of the alphabets is not
limited to the supersymmetric theories, but cluster algebras also pop-up
in QCD amplitudes. We consider Feynman integrals in dimensional
regularization and find numerous instances of the cluster algebra
appearance. In particular, we identify the alphabet of Higgs plus jet
amplitudes as C2 cluster algebra, and we find further restrictions on
the relevant space of generalized polylogarithms from the cluster
adjacency principle.