Abstract
We give a brief review of deformed N = 8 supersymmetric mechanics as a generalization of SU(2|1) mechanics. It is based on the worldline realizations of the supergroups SU(2|2) and SU(4|1) in the appropriate N = 8 , d = 1 superspaces. The corresponding models are deformations of the standard N = 8 mechanics models by a mass parameter m.
Highlights
There has been a growth in interest in deformed models of supersymmetric quantum mechanics (SQM) based on some semisimple superalgebras treated as deformations of flat d = 1 supersymmetries with the same number of supercharges
Using d = 1 superfield approaches, we explained, on a few specific examples, how to construct models of the SU(2|2) supersymmetric mechanics based on the multiplet (5, 8, 3), as well as models of SU(4|1) supersymmetric mechanics based on the multiplets (2, 8, 6) and (8, 8, 0)
All three multiplets are described by chiral superfields subjected to some extra SU(2|2) and SU(4|1) covariant constraints
Summary
The systematic study of SU(2|1) supersymmetric mechanics initiated in [8] was based on the deformation (the standard N = 2, d = 1 Poincaré superalgebra is written as { Q, Q} = 2H and, together with the U(1) automorphism generator, can be identified with the superalgebra u(1|1). We avoid calculation of the deformed covariant derivatives D I , D J (they in general involve complicated U(4) connection terms) and consider the multiplets (2, 8, 6) and (8, 8, 0) using the chiral superspace description. It should be noted, that the most general construction for the multiplet (8, 8, 0) is achieved within the SU(2|1) superfield formulation [16].
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