On Generalized Statistics and Stability in $\mathbb{Z}_2^2$-Graded Supersymmetric Yang-Mills Theory
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913066613997568 |
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| author | Ito, Ren Nago, Akio Tanigawa, Shou |
| author_facet | Ito, Ren Nago, Akio Tanigawa, Shou |
| contents | In the standard formulation of relativistic quantum field theory, a $\mathbb{Z}_2$-graded structure is assumed to realize locality and the boson-fermion dichotomy. While $\mathbb{Z}_2^n$-graded extensions are known to be allowed at the level of symmetry, their realization in interacting quantum field theories remains unclear.
In this paper, we construct a classical minimal $\mathbb{Z}_2^2$-graded supersymmetric Yang-Mills theory. We derive the invariant action and show that all kinetic terms have the correct sign, indicating the absence of classical ghost-like instabilities. Moreover, the positivity of the Hamiltonian follows from the $\mathbb{Z}_2^2$-graded supersymmetry algebra.
As a result, we show that $\mathbb{Z}_2^2$-graded generalized statistics can be realized at the classical level in a stable interacting supersymmetric gauge theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19415 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Generalized Statistics and Stability in $\mathbb{Z}_2^2$-Graded Supersymmetric Yang-Mills Theory Ito, Ren Nago, Akio Tanigawa, Shou High Energy Physics - Theory Mathematical Physics In the standard formulation of relativistic quantum field theory, a $\mathbb{Z}_2$-graded structure is assumed to realize locality and the boson-fermion dichotomy. While $\mathbb{Z}_2^n$-graded extensions are known to be allowed at the level of symmetry, their realization in interacting quantum field theories remains unclear. In this paper, we construct a classical minimal $\mathbb{Z}_2^2$-graded supersymmetric Yang-Mills theory. We derive the invariant action and show that all kinetic terms have the correct sign, indicating the absence of classical ghost-like instabilities. Moreover, the positivity of the Hamiltonian follows from the $\mathbb{Z}_2^2$-graded supersymmetry algebra. As a result, we show that $\mathbb{Z}_2^2$-graded generalized statistics can be realized at the classical level in a stable interacting supersymmetric gauge theory. |
| title | On Generalized Statistics and Stability in $\mathbb{Z}_2^2$-Graded Supersymmetric Yang-Mills Theory |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2604.19415 |