TWISTED SUPERSPACE FOR N=D=2 SUPER BF AND YANG–MILLS WITH DIRAC–KÄHLER FERMION MECHANISM

Abstract

We propose a twisted D=N=2 superspace formalism. The relation between the twisted super charges including the BRST charge, vector and pseudoscalar super charges and the N=2 spinor super charges is established. We claim that this relation is essentially related with the Dirac–Kähler 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.