Theta -diagram technique for {mathcal {N}}=1, d=4 superfields

Abstract

We describe a diagrammatic procedure to carry out the Grassmann integration in super-Feynman diagrams of 4d theories expressed in terms of {mathcal {N}}=1 superfields. This method is alternative to the well known D-algebra approach. We develop it in detail for theories containing vector, chiral and anti-chiral superfields, with the type of interactions which occur in {mathcal {N}}=2 SYM theories with massless matter, but it would be possible to extend it to other cases. The main advantage is that this method is algorithmic; we implemented it as a Mathematica program that, given the description of a super Feynman diagram in momentum space, returns directly the polynomial in the momenta produced by the Grassmann integration.