Twisted Superspace for N=D=2 Super BF and Yang-Mills with Dirac-K\"ahler Fermion Mechanism

TL;DR

This paper introduces a twisted N=2 superspace formalism linking supercharges with the Dirac-K"ahler fermion mechanism, and constructs a twisted super Yang-Mills action related to topological field theories.

Contribution

It develops a novel twisted superspace formalism for N=2 theories, connecting supercharges with Dirac-K"ahler fermions, and constructs a twisted super Yang-Mills action.

Findings

Fermionic bilinear form corresponds to quantized BF theory.

Bosonic bilinear form yields N=2 Wess-Zumino action.

Constructed twisted N=2 super Yang-Mills action equivalent to known topological theories.

Abstract

We propose a twisted D=N=2 superspace formalism. The relation between the twisted super charges including the BRST charge, vector and pseudo scalar super charges and the N=2 spinor super charges is established. We claim that this relation is essentially related with the Dirac-K\"ahler fermion mechanism. We show that a fermionic bilinear form of twisted N=2 chiral and anti-chiral superfields is equivalent to the quantized version of BF theory with the Landau type gauge fixing while a bosonic bilinear form leads to the N=2 Wess-Zumino action. We then construct a Yang-Mills action described by the twisted N=2 chiral and vector superfields, and show that the action is equivalent to the twisted version of the D=N=2 super Yang-Mills action, previously obtained from the quantized generalized topological Yang-Mills action with instanton gauge fixing.