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arXiv · 2512.22887

Non-SUSY physics and the Atiyah-Singer index theorem

Shunrui Li·Yang Liu
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Abstract

The Atiyah-Singer index theorem, a cornerstone of modern mathematics, has traditionally been derived from supersymmetric (SUSY) physics. This paper demonstrates a direct derivation from non-supersymmetric quantum statistics by establishing a fundamental correspondence: the grand partition functions of non-interacting bosonic and fermionic systems are precisely the Chern characters of certain vector bundles. Furthermore, we generalize this correspondence to infinite dimensions, where we construct a novel mathematical framework of spectral-sheaf pairs. Within this framework, we formulate a generalized index theorem, identifying the topological index with a regularized spectral product. This work not only circumvents the need for supersymmetry but also provides a deeper unifying perspective, revealing quantum statistics as a sufficient foundation for topological invariants.

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Shunrui Li, Yang Liu. 2025-12-28. Non-SUSY physics and the Atiyah-Singer index theorem. https://arxiv.org/abs/2512.22887

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