 Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4S. V. Bolokhov and V. D. Ivashchuk Advances in Mathematical Physics, 2018, vol. 2018, issue 1 Abstract: We consider generalized Melvin‐like solutions associated with nonexceptional Lie algebras of rank 4 (namely, A4, B4, C4, and D4) 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 Hs(z) (s = 1, …, 4) of squared radial coordinate z = ρ2 obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers (n1, n2, n3, n4) = (4,6, 6,4), (8,14,18,10), (7,12,15,16), (6,10,6, 6) for Lie algebras A4, B4, C4, and D4, respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer‐valued 4 × 4 matrix ν connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in A4 case) the matrix representing a generator of the Z2‐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. Date: 2018 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:8179570 Access Statistics for this article More articles in Advances in Mathematical Physics from John Wiley & Sons |
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