Abstract
We define SU(2|1) supermultiplets described by chiral superfields having non-zero external spins with respect to SU(2) ⊂ SU(2|1) and show that their splitting into N = 2, d = 1 multiplets contains the so called “long” indecomposable N = 2, d = 1 multiplets (2, 4, 2)l. We give superfield formulation for this type of N = 2 long multiplets and construct their most general superfield action. A simple example of long N = 4, d = 1 multiplet is also considered, both in the superfield and the component formulations.
Highlights
In [1], SU (2|1) supersymmetric mechanics was proposed as a deformation of the standard N = 4 mechanics by a mass parameter m
As was shown in [13], the long N = 2 multiplet can be embedded into a generalized SU (2|1) chiral multiplet described by a chiral superfield ΦA carrying some external index A with respect to the subgroup SU (2) of the supergroup SU (2|1)
The long N = 2 multiplet [9] can be interpreted as a deformation of the pair of chiral multiplets (2, 2, 0) and (0, 2, 2) by a mass-dimension parameter, i.e. it has an extended set of component fields (2, 4, 2)l
Summary
Generalizations to N = 4 supersymmetry with various extended sets of component fields were considered in [10, 11, 12]. The long N = 2 multiplet [9] can be interpreted as a deformation of the pair of chiral multiplets (2, 2, 0) and (0, 2, 2) by a mass-dimension parameter, i.e. it has an extended set of component fields (2, 4, 2)l . The case s = 1/2 The SU (2|1) chiral superfield Φi (i = 1, 2) in the U (2) representation (1/2, 2κ) is defined by the constraints
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