N = 1 D = 3 Lifshitz-Wess-Zumino model: A paradigm of reconciliation between Lifshitz-like operators and supersymmetry

摘要

By imposing the weighted renormalization condition and the (super)symmetry requirements, we construct a Lifshitz-like extension of the three-dimensional Wess-Zumino model, with dynamical critical exponentz=2. In this context, the auxiliary fieldFplays a key role by introducing the appropriate Lifshitz operator in the bosonic sector of the theory, avoiding so undesirable time-space mixing derivatives and inconsistencies concerning the criticalzexponent, as reported in the literature. The consistency of the proposed model is verified by building explicitly the susy algebra through the Noether method in the canonical formalism. This component-field Lifshitz-Wess-Zumino model is in addition rephrased in the Lifshitz superspace, a natural modification of the conventional one. The one-loop effective potential is computed to study the possibility of symmetry breaking. It is found that supersymmetry remains intact at one-loop order, while theU(1)phase symmetry suffers a spontaneous breakdown above the critical value of the renormalization point. By renormalizing the one-loop effective potential within the cutoff regularization scheme, it is observed an improvement of the UV behavior of the theory compared with the relativistic Wess-Zumino model.