Pith Number

pith:HQPFH5BN

pith:2025:HQPFH5BNJLTC7VKORG25JWDE54

not attested not anchored not stored refs resolved

Trans-series from condensates in the non-linear sigma model

Marcos Mari\~no, Yizhuang Liu

The limit of the quartic linear sigma model provides a massless perturbative framework for the non-linear sigma model that reproduces its trans-series from condensates at next-to-leading order in 1/N.

arxiv:2507.02605 v2 · 2025-07-03 · hep-th · hep-ph

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Claims

C1strongest claim

At next-to-leading order in the 1/N expansion, this framework reproduces the perturbative contribution to the two-point function, as well as its first exponentially small correction due to the condensate of the Lagrangian operator, in full agreement with the exact non-perturbative large N solution.

C2weakest assumption

The physics at the natural UV cutoff in the full LSM decouples from the NLSM in the IR in the weak-coupling limit, allowing the perturbative framework for the LSM at the cutoff scale to connect to the one in the NLSM.

C3one line summary

A new O(N)-symmetric perturbative framework for the 2D NLSM derived from the LSM limit reproduces the perturbative two-point function and its first exponentially small condensate correction at NLO in 1/N, matching the exact large N solution while identifying the leading renormalon as UV and canceled

References

47 extracted · 47 resolved · 13 Pith anchors

[1] A. M. Polyakov, Interaction of Goldstone Particles in Two-Dimensions. Applications to Ferromagnets and Massive Yang-Mills Fields , Phys. Lett. 59B (1975) 79–81 1975

[2] E. Brezin and J. Zinn-Justin, Spontaneous Breakdown of Continuous Symmetries Near Two-Dimensions, Phys. Rev. B14 (1976) 3110 1976

[3] Parisi, On Infrared Divergences, Nucl 1979

[4] M. Beneke, Renormalons, Phys. Rept. 317 (1999) 1–142, [ hep-ph/9807443] 1999 · arXiv:hep-ph/9807443

[5] M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, QCD and Resonance Physics. Theoretical Foundations, Nucl. Phys. B 147 (1979) 385–447 1979

Cited by

2 papers in Pith

Perturbative, Nonperturbative and Exact Aspects of Crystalline Phases in the Gross-Neveu Model

Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion

Receipt and verification

First computed	2026-06-10T14:10:43.243142Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c1e53f42d4ae62fd54e89b5d4d864ef185983d3090909e843ace460cdb3f04f

Aliases

arxiv: 2507.02605 · arxiv_version: 2507.02605v2 · doi: 10.48550/arxiv.2507.02605 · pith_short_12: HQPFH5BNJLTC · pith_short_16: HQPFH5BNJLTC7VKO · pith_short_8: HQPFH5BN

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HQPFH5BNJLTC7VKORG25JWDE54 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 3c1e53f42d4ae62fd54e89b5d4d864ef185983d3090909e843ace460cdb3f04f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ac1e7395d8449805e97f253dbf8b033832296d218d2a802bae768ad58edb383",
    "cross_cats_sorted": [
      "hep-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2025-07-03T13:27:25Z",
    "title_canon_sha256": "b8febeee892c744020261862b073e4164ae6c1a6e08a7e168df5b8e5d60fedeb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.02605",
    "kind": "arxiv",
    "version": 2
  }
}