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arXiv · 2606.18641

SUSY meets pseudo-Hermiticity

Cheng-Yang Lee·Gloria Cecilia de León Morales·Julio Olmos·Carlos A. Vaquera-Araujo·Siyi Zhou
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Abstract

In this work, we construct the simplest pseudo-Hermitian quantum field theory that is supersymmetric. This is the pseudo-Hermitian Wess-Zumino model in the sense that it contains a pair of symplectic fermions (anti-commuting scalar fields) that satisfy the Klein-Gordon equation and a spin-half boson that satisfies the Dirac equation. The conventional spin-statistics theorem is circumvented through the use of pseudo-Hermitian conjugation to define field adjoints. To make the supersymmetry manifest, we formulate the pseudo-Hermitian Wess-Zumino model using the superfield formalism. These superfields are Grassmann-odd so it is not possible to construct non-vanishing cubic interactions using only these superfields. We show that this problem can be resolved by coupling the pseudo-Hermitian Wess-Zumino model with the Hermitian Wess-Zumino model while preserving supersymmetry.

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Cheng-Yang Lee, Gloria Cecilia de León Morales, Julio Olmos, Carlos A. Vaquera-Araujo, Siyi Zhou. 2026-06-17. SUSY meets pseudo-Hermiticity. https://arxiv.org/abs/2606.18641

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