Sphere path integrals for fermionic gauge fields
Abstract
We consider spin-s ≥ 3/2 complex, strictly massless fermionic gauge fields on the four-sphere, S4, which is the Euclidean continuation of de Sitter spacetime, dS4. For s=5/2, after briefly discussing different options for the quantisation of the theory on dS4, 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=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≥3/2 fermionic gauge potential. Additionally, we compute the coefficient of the logarithmic divergence of the S4 path integral for all spin-s ≥ 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=1/2, 3/2,…, observed recently.
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BibTeX
@misc{baracco2026sphere,
title = {{Sphere path integrals for fermionic gauge fields}},
author = {Chiara Baracco and Vasileios A. Letsios},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19275},
eprint = {2609.19275},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19275},
}
RIS
TY - UNPB
TI - Sphere path integrals for fermionic gauge fields
AU - Chiara Baracco
AU - Vasileios A. Letsios
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.19275
UR - https://arxiv.org/abs/2609.19275
AB - We consider spin-s ≥ 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=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=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≥3/2 fermionic gauge potential. Additionally, we compute the coefficient of the logarithmic divergence of the S^4 path integral for all spin-s ≥ 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=1/2, 3/2,…, observed recently.
ER -