Exact solutions of SL(N,R)-invariant chiral equations one- and two-dimensional subspaces

Abstract

A methodology for integrating the chiral equation (pg,&-I),,-+ (pg,g-') ,= = 0 is developed, when g is a matrix of the SL(N,R) groug. In this work the ansatze g=g(A) where A satisfy the Laplace equation and g=g(&r) are made, where A and T are geodesic parameters of an arbitrary Riemannian space. This reduces the chiral equation to an algebraic problem and g can be obtained by integrating a homogeneous linear system of differential equations. As an example of the first ansatz, all the matrices for N=3 and one example for N= 8, which corresponds to exact solutions of the d= 5 and d= 10 Kaluza-Klein theory, respectively are given. For the second ansatz the chiral equations are integrated for the subgroups SL(2,R), S0(2,1R), Sp(2,R), and the Abelian subgroups.

Class of Einstein–Maxwell phantom fields: rotating and magnetized wormholes

“…This is possible because the corresponding potential space, defined bellow, is a symmetric Riemannian space only for α = 0 and α = √ 3, but this is not the case for the low energy limit in super strings or the Maxwell-phantom theories. In [12] we extended this method [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] to the Einstein-Maxwell-Dilaton fields with arbitrary α and in this work I have extended this techniques for the Einstein-Maxwell-Phantom fields. In this work I have given a method from which we can derive a set of formulas that can be integrated in order to find exact solutions of the Einstein-Maxell phantom fields.…”

Charging symmetries and linearizing potentials for heterotic string in three dimensions

“…the KK theory obtains a chiral form. This form allowed to obtain wide classes of the three-dimensional solutions defined by a set of harmonic functions (see [17]), etc. Moreover, in two dimensions the inverse scattering transform technique leads to construction of the 2N-soliton solution (see [18] for the d = 1 and d = 2 cases).…”

Exact solutions ofG-invariant chiral equations

“…A general integration algorithm that applies even to the Lie algebra sl(N, R), is given in [8]. An explicitly solvable example for SL(4, R) can be found in [91.…”