{
  "abstract": "We describe a family of two-dimensional metric deformations that preserve integrability. The seeds are (classically) conformal integrable field theories and the deformations are directly related to different classes of auxiliary field sigma models. We introduce a master action connecting deformations by Lie-algebra-valued auxiliary fields, the so-called $ν$-frame, to deformations by two Lorentz-charged scalars. These auxiliary scalar fields can be identified as Beltrami differentials of an auxiliary two-dimensional metric, providing a direct connection with the metric approach to $T\\bar{T}$-like deformations. For Weyl-invariant seed matter theories, the auxiliary metric sector is described by a reduced gravitational potential. We show that the resulting framework preserves classical Lax integrability whenever the seed matter theory admits a Lax representation of its equations of motion on a generic curved two-dimensional spacetime. Finally, within the Lorentz-invariant family and the zweibein deformations of conformal matter theories considered here, we identify $T\\bar{T}$ as the only deformation that can be interpreted as a field-dependent coordinate transformation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13501",
  "author_total": 4,
  "authors": [
    {
      "name": "Nicola Baglioni"
    },
    {
      "name": "Daniele Bielli"
    },
    {
      "name": "Parita Shah"
    },
    {
      "name": "Gabriele Tartaglino-Mazzucchelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d204ny5r520kk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13501",
  "fulltext_url": null,
  "id": "d204ny5r520kk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13501",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7221515890",
  "pdf_url": "https://arxiv.org/pdf/2610.13501",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d204ny5r520kk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.13501",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13501"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Integrable auxiliary field sigma model and the metric approach to $T\\bar{T}$-like deformations",
  "title_text": "Integrable auxiliary field sigma model and the metric approach to TT̅-like deformations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/d204ny5r520kk",
  "venue": "arXiv",
  "versions": []
}