arXiv 1806.014812018-06hep-th

$\mathcal{N}=1$ $\mathcal{D}=3$ Lifshitz-Wess-Zumino模型：类Lifshitz算子与超对称性协调的一个范例

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

E. A. Gallegos

备注：: Published version in Physics Letters B (2019)
发表信息：: Physics Letters B 793 (2019) 372-382
DOI：: 10.1016/j.physletb.2019.05.001

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摘要：

通过引入加权重正化条件和（超）对称性要求，构造了三维Wess-Zumino模型的Lifshitz型推广，动力学临界指数z=2.在这种情况下，辅助字段F起着关键作用，通过引入适当的Lifshitz运营商的玻色子部门的理论，避免如此不良的时空混合衍生物和不一致的临界z指数，如文献中所报道的。该模型的一致性验证了明确建立的susy代数通过规范形式主义的Noether方法。这个分量场Lifshitz-Wess-Zumino模型在Lifshitz超空间中也被改写，这是对传统模型的自然修改。计算了单圈有效势，研究了对称性破缺的可能性。结果表明，超对称性在单圈阶时保持不变，而U（1）相对称性在重整化点的临界值以上发生自发击穿。通过在截断正则化方案中重整化单圈有效势，观察到与相对论Wess-Zumino模型相比，该理论的UV行为有所改善。

英文摘要：

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 exponent z=2. In this context, the auxiliary field F plays 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 critical z exponent, 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 the U(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.

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