https://doi.org/10.1140/epjp/s13360-021-01193-6
Regular Article
On generalized Melvin solutions for Lie algebras of rank 4
1
Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198, Moscow, Russian Federation
2
Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya St., 119361, Moscow, Russian Federation
Received:
20
December
2020
Accepted:
3
February
2021
Published online:
17
February
2021
We deal with generalized Melvin-like solutions associated with Lie algebras of rank 4 (
, 
, 
, 
, 
). Any solution has static cylindrically symmetric metric in D dimensions in the presence of four Abelian two-form 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 are polynomials of powers 
for Lie algebras , , , , , respectively. The asymptotic behaviour for the polynomials at large z is governed by an 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 studied. We also present two-form flux integrals over a two-dimensional submanifold. Dilatonic black hole analogs of the obtained Melvin-type solutions, e.g. “phantom” ones, are also considered. The phantom black holes are described by fluxbrane polynomials under consideration.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
