N = 2 Supersymmetry and the Irreducible SU (2) ‐Extended Superfields

The structure of the irreducible SU (2)‐extended superfields in the usual N = 2 superspace is investigated in detail. We derive the irreducible superfield contents of a general N = 2 scalar superfield and give the complete off‐shell component description of all the irreducible N = 2 scalar superfields, by considering N = 2 supersymmetry as the SU (2)‐invariant combination of two simple N = 1 supersymmetries. We give also the systematic method of explicit construction of any irreducible N = 2 superfield with external SL (2, C) ⊗ SU (2) index on the basis of the solution to all the irreducible scalar N = 2 superfields. To demonstrate the applications of the method, the linearized N = 2 conformal and Poincaré supergravities are rederived. We apply N = 2 superapace methods to construct various non‐linear sigma models with extended supersymmetry. The latter are proved to be non‐renormalizable in the four‐dimensional space‐time, but finite to all orders in a perturbation theory in two space‐time dimensions. The couplings of N = 2 nonlinear sigma models under consideration to N = 2 super‐Yang‐Mills fields are diacuseed too. In conclusion, an outline of the similar approach to the construction of the irreducible superfields in N = 4 superspace is given. The article can be viewed as the Introduction to N = 2 superspace.