Feynman Rules in N = 2 projective superspace III : Yang - Mills

The kinetic action of the N = 2 Yang-Mills vector multiplet can be written in projective N = 2 superspace using projective multiplets. It is possible to perform a simple N = 2 gauge fixing, which translated to N = 1 component language makes the kinetic terms of gauge potentials invertible. After coupling the Yang-Mills multiplet to unconstrained sources it is very simple to integrate out the gauge fixed vector multiplet from the path integral of the free theory and obtain the N = 2 propagator. Its reduction to N = 1 components agrees with the propagators of the gauge fixed N = 1 component superfields. The coupling of Yang-Mills multiplets and hypermultiplets in N = 2 projective superspace allows us to define Feynman rules in N = 2 superspace for these two fields.