Duality identities for moduli functions of generalized Melvin solutions related to classical Lie algebras of rank 4
type: Item
instance of: scholarly article
title: Duality identities for moduli functions of generalized Melvin solutions related to classical Lie algebras of rank 4
zbMATH Open document ID: 1440.83009
DOI: 10.1155/2018/8179570
author: S. V. Bolokhov
author: V. D. Ivashchuk
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: We consider generalized Melvin-like solutions associated with nonexceptional Lie algebras of rank \(4\) (namely, \(A_4\), \(B_4\), \(C_4\), and \(D_4\)) corresponding to certain internal symmetries of the solutions. The system under consideration is a static cylindrically symmetric gravitational configuration in \(D\) dimensions in presence of four Abelian 2-forms and four scalar fields. The solution is governed by four moduli functions \(H_s(z)\) (\(s = 1, \ldots, 4\)) of squared radial coordinate \(z = \rho^2\) obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers \((n_1, n_2, n_3, n_4) = (4,6, 6,4),(8,14,18,10),(7,12,15,16),(6,10,6, 6)\) for Lie algebras \(A_4\), \(B_4\), \(C_4\), and \(D_4\), respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued \(4 \times 4\) matrix \(\nu\) connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in \(A_4\) case) the matrix representing a generator of the \(\mathbb{Z}_2\)-group of symmetry of the Dynkin diagram. The symmetry properties and duality identities for polynomials are obtained, as well as asymptotic relations for solutions at large distances. We also calculate 2-form flux integrals over \(2\)-dimensional discs and corresponding Wilson loop factors over their boundaries.
Mathematics Subject Classification ID: 83C50
zbMATH DE Number: 6992025
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8179570
OpenAlex ID: W2900228798
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Wikidata QID: Q128968059
description: scientific article; zbMATH DE number 6992025