Grope cobordism and feynman diagrams

Grope Cobordism and Feynman Diagrams

We explain how the usual algebras of Feynman diagrams behave under the grope degree introduced in [CT]. We show that the Kontsevich integral rationally classifies grope cobordisms of knots in 3-space when the “class” is used to organize gropes. This implies that the grope cobordism equivalence relations are highly nontrivial in dimension 3. We also show that the class is not a useful organizing...

Grope Cobordism of Classical Knots

Motivated by the lower central series of a group, we define the notion of a grope cobordism between two knots in a 3-manifold. Just like an iterated group commutator, each grope cobordism has a type that can be described by a rooted unitrivalent tree. By filtering these trees in different ways, we show how the Goussarov-Habiro approach to finite type invariants of knots is closely related to ou...

Feynman diagrams versus Fermi-gas Feynman emulator

Matrix Theory and Feynman Diagrams

We briefly review the computation of graviton and antisymmetric tensor scattering amplitudes in Matrix Theory from a diagramatic S-Matrix point of view. It is by now commonly believed that eleven dimensional supergravity is the low-energy effective theory of a more fundamental microscopic model, known as M-theory. A proposed definition of M-theory has been given in terms of the large N limit of...

Scattering equations and Feynman diagrams

We show a direct matching between individual Feynman diagrams and integration measures in the scattering equation formalism of Cachazo, He and Yuan. The connection is most easily explained in terms of triangular graphs associated with planar Feynman diagrams in φ3-theory. We also discuss the generalization to general scalar field theories with φp interactions, corresponding to polygonal graphs ...