N=2 Super Yang-Mills: Auxiliary Fields Question

[StuartY]

I was wondering since the Vector supermultiplet in N=2 SUSY can be built from a Chiral and a Vector supermultiplet from N=1, in order to make up the off-shell degrees of freedom, would you include the two auxiliary fields from the N=1 theory (traditionally F from the Chiral and D from the vector multiplets), or would you make them up using a single auxiliary field? I'm sorry if this was a terrible question or has been poorly worded.

 

[haushofer]

I'm not familiar with N=2 SYM, but what does your off-shell counting suggest?

 

[StuartY]

Sorry for the late reply. So off-shell for N=1 requires 2 bosonic d.o.f. for the chiral superultiplet, and 1 for the vector. For N=2 the vector supermultiplet requires 3 bosonic d.o.f.. I've been looking at this some more, and I think I'm getting even more confused because when I try and write out a Lagrangian for the N=2 vector supermultiplet I get the same Lagrangian as for the N=1 gauge theory.