{
  "id": "2304.11346",
  "version": "v1",
  "published": "2023-04-22T08:16:11.000Z",
  "updated": "2023-04-22T08:16:11.000Z",
  "title": "The Yang-Mills-Higgs functional on complex line bundles: asymptotics for critical points",
  "authors": [
    "Giacomo Canevari",
    "Federico Luigi Dipasquale",
    "Giandomenico Orlandi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a gauge-invariant Ginzburg-Landau functional (also known as Abelian Yang-Mills-Higgs model) on Hermitian line bundles over closed Riemannian manifolds of dimension $n \\geq 3$. Assuming a logarithmic energy bound in the coupling parameter, we study the asymptotic behaviour of critical points in the non-self dual scaling, as the coupling parameter tends to zero. After a convenient choice of the gauge, we show compactness of finite-energy critical points in Sobolev norms. Moreover, %independently of the gauge andthanks to a suitable monotonicity formula,we prove that the energy densities of critical points, rescaled by the logarithm of the coupling parameter, concentrate towards the weight measure of a stationary, rectifiable varifold of codimension~2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-22T08:16:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical points",
      "complex line bundles",
      "yang-mills-higgs functional",
      "asymptotic",
      "coupling parameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}