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- Title
On Fluxbrane Polynomials for Generalized Melvin-like Solutions Associated with Rank 5 Lie Algebras.
- Authors
Bolokhov, Sergey V.; Ivashchuk, Vladimir D.
- Abstract
We consider generalized Melvin-like solutions corresponding to Lie algebras of rank 5 ( A 5 , B 5 , C 5 , D 5 ). 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 H s (z) ( s = 1 ,... , 5 ) of squared radial coordinates z = ρ 2 , which obey five differential master equations. The moduli functions are polynomials of powers (n 1 , n 2 , n 3 , n 4 , n 5) = (5 , 8 , 9 , 8 , 5) , (10 , 18 , 24 , 28 , 15) , (9 , 16 , 21 , 24 , 25) , (8 , 14 , 18 , 10 , 10) for Lie algebras A 5 , B 5 , C 5 , D 5 , 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 A 5 and D 5 cases) with the matrix representing a generator of the Z 2 -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.
- Subjects
LIE algebras; POLYNOMIALS; DYNKIN diagrams; MATRIX inversion; SCALAR field theory; SYMMETRY groups; ABELIAN functions
- Publication
Symmetry (20738994), 2022, Vol 14, Issue 10, pN.PAG
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym14102145