Abstract
We consider a Galilean mathcal{N}=2 supersymmetric theory with F-term couplings in 2 + 1 dimensions, obtained by null reduction of a relativistic Wess-Zumino model. We compute quantum corrections and we check that, as for the relativistic parent theory, the F-term does not receive quantum corrections. Even more, we find evidence that the causal structure of the non-relativistic dynamics together with particle number conservation constrain the theory to be one-loop exact.
Highlights
In the relativistic setting the construction of SUSY invariant actions and the study of renormalization properties is better performed in superspace, where fields belonging to the same multiplet are organized in superfields
Since the non-relativistic limit via null reduction technique does not modify the grassmannian part of the superfields in the action, R-symmetry works in the same way as in the relativistic case
In this paper we studied the renormalization properties of a 2 + 1 dimensional model with S2G Galilean SUSY invariance, obtained by null reduction of the four-dimensional relativistic Wess-Zumino model (see eq (4.1))
Summary
We are interested in studying non-relativistic SUSY theories in 2 + 1 dimensions with S2G invariance This graded generalization of the Galilean algebra contains two complex supercharges and is described by the following non-vanishing (anti)commutators [Pj, Kk] = iδjkM , [Pj, J ] = −i jkPk ,. The central charge M corresponds to the mass or particle number conservation This is the non-relativistic N = 2 SUSY algebra in (2+1) dimensions. While in the relativistic reduction a central term appears in the fermionic part of the algebra when we reduce the number of dimensions, in the non-relativistic case the central charge is produced already in the bosonic sector (without requiring any SUSY extension) and accounts for the physical fact that in non-relativistic theories the particle number is a conserved quantity
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