Further investigations into the graph theory of $\phi^4$-periods and the $c_2$ invariant

Source abstract

A Feynman period is a particular residue of a scalar Feynman integral which is both physically and number theoretically interesting. Two ways in which the graph theory of the underlying Feynman graph can illuminate the Feynman period are via graph operations which are period invariant and other graph quantities which predict aspects of the Feynman period, one notable example is known as the c_2 invariant. We give results and computations in both these directions, proving a new period identity and computing its consequences up to 11 loops in \phi^4 -theory, proving a c_2 invariant identity, and giving the results of a computational investigation of c_2 invariants at 11 loops.