On generalized Melvin’s solutions for Lie algebras of rank 2

We consider a class of solutions in multidimensional gravity which generalize Melvin’s well-known cylindrically symmetric solution, originally describing the gravitational field of a magnetic flux tube. The solutions considered contain the metric, two Abelian 2-forms and two scalar fields, and are governed by two moduli functions H1(z) and H2(z) (z = ρ2, ρ is a radial coordinate) which have a polynomial structure and obey two differential (Toda-like) master equations with certain boundary conditions. These equations are governed by a certain matrix A which is a Cartan matrix for some Lie algebra. The models for rank-2 Lie algebras A2, C2 and G2 are considered. We study a number of physical and geometric properties of these models. In particular, duality identities are proved, which reveal a certain behavior of the solutions under the transformation ρ → 1/ρ; asymptotic relations for the solutions at large distances are obtained; 2-form flux integrals over 2-dimensional regions and the corresponding Wilson loop factors are calculated, and their convergence is demonstrated. These properties make the solutions potentially applicable in the context of some dual holographic models. The duality identities can also be understood in terms of the Z2 symmetry on vertices of the Dynkin diagram for the corresponding Lie algebra. © 2017, Pleiades Publishing, Ltd.

Authors
Number of issue
4
Language
English
Pages
337-342
Status
Published
Volume
23
Year
2017
Organizations
  • 1 Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia (RUDN University), ul. Miklukho-Maklaya 6, Moscow, 117198, Russian Federation
  • 2 Center for Gravitation and Fundamental Metrology, VNIIMS, Ozyornaya ul. 46, Moscow, 119361, Russian Federation
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/5280/
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