{
  "abstract": "We develop a continuum framework for comparing the Gribov--Zwanziger and center-vortex descriptions of confinement through the gauge-invariant twisted partition function of the electric $\\mathbb{Z}_N^{[1]}$ 1-form symmetry. A background 2-form field $B$, equivalently an 't~Hooft twist on a torus, labels a global sector and is not itself a dynamical center vortex. For a minimal irreducible twist on $T^4$, we derive the complete adjoint momentum lattice of $SU(N)$. The twisted spectrum is exactly the scalar spectrum on an enlarged torus with periods $(L_1,L_2,NL_3,NL_4)$ with the ordinary-torus sublattice removed. This yields a finite Faddeev--Popov gap at the flat representative and reduces twisted-minus-untwisted spectral traces to ordinary torus traces. For the refined Gribov--Zwanziger (RGZ) kernel, Poisson resummation gives an exact finite-volume Bessel-function winding sum with a universal center-twist projector. We evaluate the Gaussian one-loop integral at fixed RGZ parameters up to the finite-dimensional global zero-mode/stabilizer normalization. The Zwanziger determinants cancel, while the gauge-fixing/ghost sector leaves a universal massless primed determinant on $T^4$; the untwisted sector also contains constant gluon modes. The only normalization not fixed by the local quadratic Hessian is the relative zero-mode/stabilizer measure of the reducible untwisted and irreducibly twisted flat connections. We also derive closed finite-volume sources for the RGZ stationary equations. The massive response is exponentially suppressed at large volume, whereas the massless factor depends on the global zero-mode normalization. Thus the Gaussian calculation does not by itself establish the strong center-vortex-condensation criterion for $Z[B]/Z[0]$, but it isolates the remaining global normalization problem and separates a global twist from an actual dynamical vortex.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03525",
  "author_total": 1,
  "authors": [
    {
      "name": "Okuto Morikawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1h7bnpcct1das.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03525",
  "fulltext_url": null,
  "id": "1h7bnpcct1das",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03525",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-lat"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7208713227",
  "pdf_url": "https://arxiv.org/pdf/2609.03525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1h7bnpcct1das.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.03525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03525"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    }
  ],
  "title": "Center-twisted Gribov spectra and the finite-volume Gaussian response in the refined Gribov--Zwanziger framework",
  "title_text": "Center-twisted Gribov spectra and the finite-volume Gaussian response in the refined Gribov--Zwanziger framework",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:26Z",
  "url": "https://research.draconitic.com/paper/1h7bnpcct1das",
  "venue": "arXiv",
  "versions": []
}