{
  "id": "2012.13001",
  "version": "v1",
  "published": "2020-12-23T22:05:52.000Z",
  "updated": "2020-12-23T22:05:52.000Z",
  "title": "On fluxbrane polynomials for generalized Melvin-like solutions associated with rank 5 Lie algebras",
  "authors": [
    "S. V. Bolokhov",
    "V. D. Ivashchuk"
  ],
  "comment": "13 pages, 1 figure, LaTex. arXiv admin note: substantial text overlap with arXiv:1912.08083, arXiv:1709.09663",
  "categories": [
    "hep-th",
    "gr-qc"
  ],
  "abstract": "We consider generalized Melvin-like solutions corresponding to Lie algebras of rank $5$ ($A_5$, $B_5$, $C_5$, $D_5$). The solutions take place in $D$-dimensional gravitational model with five Abelian 2-forms and five scalar fields. They are governed by five moduli functions $H_s(z)$ ($s = 1,...,5$) of squared radial coordinate $z=\\rho^2$ obeying five differential master equations. The moduli functions are polynomials of powers $(n_1, n_2, n_3, n_4, n_5) = (5,8,9,8,5), (10,18,24,28,15), (9,16,21,24,25), (8,14,18,10,10)$ for Lie algebras $A_5$, $B_5$, $C_5$, $D_5$ respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued $5 \\times 5$ matrix $\\nu$ connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in $A_5$ and $D_5$ cases) with the matrix representing a generator of the $\\mathbb{Z}_2$-group of symmetry of the Dynkin diagram. The symmetry and duality identities for polynomials are obtained, as well as asymptotic relations for solutions at large distances.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-23T22:05:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie algebra",
      "generalized melvin-like solutions",
      "fluxbrane polynomials",
      "large distances",
      "moduli functions"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}