Abstract
We find a formulation of $\mathcal{N}=2$ supersymmetric Yang-Mills theory in Projective superspace. In particular we find an expression for the field strength in terms of an unconstrained prepotential which is desirable when quantizing the theory. We use this to write the action in terms of the prepotential and show that it reduces to the known result in the abelian limit.
Highlights
Projective superspace [1] is a manifestly supersymmetric formalism for theories with eight supercharges
The fact that the projective superspace formalism is closely connected with the twistor space description of hyperkähler manifolds [2,3,4] or quaternion Kähler manifolds [5] has led to many applications in mathematics and physics
In three appendices we review known results that are crucial for this paper; we show how from extracting the divergent part of a one loop calculation with a hypermultiplet coupled to a background gauge field, we can extract a closed form for the Yang-Mills action expressed in terms of a projective prepotential
Summary
Projective superspace [1] is a manifestly supersymmetric formalism for theories with eight supercharges. A hybrid formalism between the projective and harmonic superspaces has been constructed [25,26,27,28,29] called hyperspace Using these new tools the authors were able to derive several new results for projective superspace, in particular for non-Abelian Yang-Mills theory formulated in projective superspace. In particular we derive an expression for the Yang-Mills field strength in terms of the gauge prepotential superfield and show that it has the correct properties. In three appendices we review known results that are crucial for this paper; we show how from extracting the divergent part of a one loop calculation with a hypermultiplet coupled to a background gauge field, we can extract a closed form for the Yang-Mills action expressed in terms of a projective prepotential. In the final appendix we discuss aspects of the ε-prescription introduced in [25] which is an integral part of the techniques used to prove the results of this article
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