{
  "abstract": "We introduce a two-coupling generalization of $\\mathbb{C}P^{N-1}$ model that continuously interpolates between the self-dual ($ε=0$) and the physical ($ε=g$) theories as a useful nonperturbative tool. At $ε\\neq g$, this model possesses a chiral imbalance, which may be viewed as a real topological deformation (imaginary-$θ$). We demonstrate that exact quantum equivalence between first- and second-order formulations strictly requires a topological counterterm sourced by a bosonic chiral anomaly. Solving this deformed theory at large $N$ yields two primary results. First, we analytically determine the nonperturbative vacuum structure of the self-dual theory, a self-dual vacuum with a dynamically generated field-strength condensate. Second, we resolve a fundamental paradox where saddles with $(θ+ 2πn) \\sim O(N)$ ($n$ is branch number) spuriously yield lower energy densities than the physical ground state. Because the effective action possesses an essential singularity at $F=0$, we show that the Lefschetz thimble analysis must be generalized to include boundary thimbles. A boundary Stokes phenomenon renders the problematic saddles topologically inactive, fully restoring the validity of the large-$N$ expansion for strongly coupled theories.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30160",
  "author_total": 2,
  "authors": [
    {
      "name": "Yui Hayashi"
    },
    {
      "name": "Mithat Ünsal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2wxf9c4tmbnqg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30160",
  "fulltext_url": null,
  "id": "2wxf9c4tmbnqg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30160",
  "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": "W7204956257",
  "pdf_url": "https://arxiv.org/pdf/2608.30160",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2wxf9c4tmbnqg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.30160",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30160"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    }
  ],
  "title": "From Self-Dual to Physical $\\mathbb{C}P^{N-1}$: Anomalies, Boundary Stokes Phenomenon, and Global Structure of $θ$-vacua",
  "title_text": "From Self-Dual to Physical ℂP^N−1: Anomalies, Boundary Stokes Phenomenon, and Global Structure of θ-vacua",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/2wxf9c4tmbnqg",
  "venue": "arXiv",
  "versions": []
}