Abstract
Starting from N = 1 scalar supermultiplets in (2+1) dimensions, webuild explicitly the composite superpartners which define an N = 2superalgebra induced by the initial N = 1 supersymmetry. The occurrence ofthis extension is linked to the topologically conserved current out of whichthe composite superpartners are constructed.
Highlights
25.2 constituent fields, can be elevated to an N = 2 supersymmetry in terms of suitably constructed composite fields
In three space-time dimensions, on the other hand, the photons have only a single degree of freedom and they are allowed, in a sense, to get a v.e.v without breaking Lorentz symmetry. It is this fact that allows the extension of such ideas in (2+1) dimensions to incorporate supersymmetry, which is intimately related to Lorentz invariance
From a physical point of view, with relevance to strongly correlated electrons, we remark that the maintainance of Lorentz symmetry is connected with the fact that we restrict our attention to excitations near nodes of the Fermi surface of such systems [6], which exhibit relativistic behaviour, with the role of the velocity of ‘light’ played by the Fermi velocity at the node
Summary
We expose the procedure of adding higher-order composites so as to generate the coupling between the scalar and vector supermultiplets, which implies the N = 2 structure of the transformations. We will construct explicitly the covariant derivative of φc by adding to the complex quadratic scalar field a higher-order composite which will generate the minimal coupling.
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