Diagonal trace identities for bosonic and fermionic matrices

Haoran Zhu

Abstract

We determine the second stabilised diagonal of finite-rank fermionic trace relations in the $\partial\psi$ model. In this paper, the formal letters of the model are treated as independent odd matrix letters, denoted $\psi_0,\psi_1,\psi_2,\ldots$. For every $N\geqslant 2$, the charge-$2N+2$ relation space at rank $N$ has odd dimension $4$ and even dimension $4$. More precisely, it has a basis consisting of the eight signed polarised Cayley--Hamilton trace identities obtained by inserting copies of the even word $\psi_0^2$. This proves a conjecture of Eleftheriou, Ji, and Murthy.

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Archived 1 October 2026 (Pacific time)

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@article{Zhu2026DiagonalTrace,
  author={Zhu, Haoran},
  title={Diagonal trace identities for bosonic and fermionic matrices},
  journal={Theoretical and Mathematical Physics (to appear)},
  year={2026},
  url={https://haoran-horace-zhu.github.io/papers/diagonal-trace-identities/v1.html},
  note={Archived copy, version 1}
}

Abstract

Archive history

Archive version 1 This archived copy

Citation