A relation between deformed superspace and Lee-Wick higher-derivative theories

• Published in: Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2015-07, Vol.48 (27), p.275403-12
• Main Authors: Dias, M, Ferrari, A F, Palechor, C A, Senise Jr, C R
• Format: Article
• Language: English
• Subjects: Deformation; higher-derivative theories; Mathematical models; noncommutative theories; Preserves; Proposals; Standard model (particle physics); Supersymmetry
• ISSN: 1751-8113; 1751-8121
• DOI: 10.1088/1751-8113/48/27/275403

We propose a non-anticommutative superspace that relates to the Lee-Wick type of higher-derivative theories, which are known for their interesting properties and have led to proposals of phenomenologically viable higher-derivative extensions of the Standard Model. The deformation of superspace we consider does not preserve supersymmetry or associativity in general, but, we show that a non-anticommutative version of the Wess-Zumino model can be properly defined. In fact, the definition of chiral and antichiral superfields turns out to be simpler in our case than in the well known supersymmetric case. We show that when the theory is truncated at the first nontrivial order in the deformation parameter, supersymmetry is restored, and we end up with a well-known Lee-Wick type of higher-derivative extension of the Wess-Zumino model. Thus, we show how non-anticommutativity could provide an alternative mechanism for generating these higher-derivative theories.