Affiliation:
1. Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198 Moscow, Russia
2. Center for Gravitation and Fundamental Metrology, All-Russian Research Institute of Metrological Service (VNIIMS), 46 Ozyornaya St., 119361 Moscow, Russia
Abstract
We consider generalized Melvin-like solutions corresponding to Lie algebras of rank 5 (A5, B5, C5, D5). The solutions take place in a D-dimensional gravitational model with five Abelian two-forms and five scalar fields. They are governed by five moduli functions Hs(z) (s=1,...,5) of squared radial coordinates z=ρ2, which obey five differential master equations. The moduli functions are polynomials of powers (n1,n2,n3,n4,n5)=(5,8,9,8,5),(10,18,24,28,15),(9,16,21,24,25),(8,14,18,10,10) for Lie algebras A5, B5, C5, D5, respectively. The asymptotic behavior for the polynomials at large distances is governed by some integer-valued 5×5 matrix ν connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in A5 and D5 cases) with the matrix representing a generator of the Z2-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.
Funder
RUDN University Strategic Academic Leadership Program
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
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