On fluxbrane polynomials for generalized Melvin-like solutions associated with rank 5 Lie algebras

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 $D$-dimensional gravitational model with five Abelian 2-forms and five scalar fields. They are governed by five moduli functions $H_s(z)$ ($s=1,...,5$) of squared radial coordinate $z={\rho }^2$ 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 behaviour for the polynomials at large distances is governed by some integer-valued $5\times 5$ matrix $\nu$ 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 ${\mathbb{Z}}_2$-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.

arXiv comment14 pages, 1 figure, LaTex. Three references are added, and three references (self-citations) are deleted, two paragraphs are added to Introduction and Section 3. Conclusions are slightly enlarged. The total list of polynomials is moved to Appendix

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• Fluxbrane polynomials and Melvin-like solutions for simple Lie algebras