Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4

S. V. Bolokhov and V. D. Ivashchuk

Advances in Mathematical Physics, 2018, vol. 2018, 1-10

Abstract:

We consider generalized Melvin-like solutions associated with nonexceptional Lie algebras of rank (namely, , , , and ) corresponding to certain internal symmetries of the solutions. The system under consideration is a static cylindrically symmetric gravitational configuration in dimensions in presence of four Abelian 2-forms and four scalar fields. The solution is governed by four moduli functions ( ) of squared radial coordinate obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers for Lie algebras , , , and , respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued matrix connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in case) the matrix representing a generator of the - 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 - dimensional discs and corresponding Wilson loop factors over their boundaries.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:8179570

DOI: 10.1155/2018/8179570

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