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Sphere path integrals for fermionic gauge fields — arXiv:2609.19275

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.19275
License (as archived): CC0-1.0
Archived: 2026-10-10T06:14:48.575Z
SHA-256 of the archived text: 27b9fcd07ffee3e256da697ea4b01ab9ab911e8c25b83a675811e145f2c6e07a
Stable URL of this page: https://metraipolis.com/documento/dc_cdee313eb8ba

How to cite

Sphere path integrals for fermionic gauge fields — arXiv:2609.19275 — arXiv (en), https://arxiv.org/abs/2609.19275 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cdee313eb8ba (Metraipolis archive dc_cdee313eb8ba, sha256 27b9fcd07ffee3e256da697ea4b01ab9ab911e8c25b83a675811e145f2c6e07a)

BibTeX

@misc{dccdee313eb8ba,
  title = {Sphere path integrals for fermionic gauge fields — arXiv:2609.19275},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.19275},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cdee313eb8ba; sha256 27b9fcd07ffee3e256da697ea4b01ab9ab911e8c25b83a675811e145f2c6e07a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.19275. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We consider spin-$s \geq \frac{3}{2}$ complex, strictly massless fermionic gauge fields on the four-sphere, $S^4$, which is the Euclidean continuation of de Sitter spacetime, dS$_4$. For $s=\frac{5}{2}$, after briefly discussing different options for the quantisation of the theory on dS$_4$, we compute the one-loop sphere path integral. We explain how it can be expressed in terms of functional determinants, generalising previous results for $s=\frac{3}{2}$. We proceed to rewrite the result in terms of `bulk' unitary Harish-Chandra characters in the discrete series of the de Sitter isometry group, $Spin(4,1)$, and `edge' characters. We then generalise the character expression of the sphere path integral for any complex, strictly massless spin-$s\geq\frac{3}{2}$ fermionic gauge potential. Additionally, we compute the coefficient of the logarithmic divergence of the $S^4$ path integral for all spin-$s \geq \frac{3}{2}$, and we show that it is fully encoded by bulk and edge characters. We further show that at one loop no imaginary phase appears for strictly massless fermionic gauge potentials, contrary to the case of bosons. Lastly, we confirm the exact one-loop cancellation between bulk and edge contributions for the case of an infinite tower of complex massless fermions of spins $s=\frac{1}{2}, \frac{3}{2},\dots$, observed recently.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-18 in gr-qc).
Categorie arXiv: High Energy Physics - Theory (hep-th) ; General Relativity and Quantum Cosmology (gr-qc).
Pagina del lavoro: https://arxiv.org/abs/2609.19275 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-10T05:51:02.722Z dalla pagina https://arxiv.org/catchup/gr-qc/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).