FromN=1toN=2supersymmetries in 2+1 dimensions

Abstract

Starting from N = 1 scalar and vector supermultiplets in 2+1 dimensions, we construct superfields which constitute Lagrangians invariant under N = 2 supersymmetries. We first recover the N = 2 supersymmetric Abelian-Higgs model and then the N = 2 pure super Yang-Mills model. The conditions for this elevation are consistent with previous results found by other authors. N = 2 supersymmetry in 2+1 dimensions had been studied [1] in order to investigate the supersymmetrization of the instantons effects which lead to a linear confinement [2]. Since then, systematic studies of N = 2 supersymmetry in 2+1 dimensions have been done in [3] where exact results were obtained, such as superpotentials and topologies of moduli spaces in various cases.These exact results can be derived since N = 2 supersymmetry in 2+1 dimensions can be obtained by dimensional reduction of N = 1 supersymmetry in 3+1 dimensions [4] and thus has similar properties, such as non-renormalization theorems. These theorems are not present for N = 1 supersymmetry in 2+1 dimensions and it is thus interesting to study its elevation to N = 2. In this context, it was shown that the presence of topologically conserved currents leads to a centrally extended N = 2 superymmetry, the central charge of the superalebra being the topological charge [5]. In [6], the N = 1 supersymmetric Abelian-Higgs model was considered and it was shown that the on-shell Lagrangian can be extended to the N = 2 Abelian-Higgs model if a relation is imposed between the gauge coupling and the Higgs self-coupling. Such a condition is in general expected in a N = 2 invariant theory built out of N = 1 Lagrangians [7]. Another example of extension was 1

-theory on Spin(7) manifolds, fluxes and 3D, =1 supergravity

“…For this reason the component form of three-dimensional N = 2 supergravity is known. Although there has been much activity in three dimensions [1,2,3,4,5,6,7,8,9], there is no general off-shell component or superspace formulation of three-dimensional N = 1 supergravity in the literature. There are, however, on-shell realisations with N ≥ 1 given in [10,11].…”