Toward Interactions through Information in a Multifractal Paradigm

In a multifractal paradigm of motion, Shannon’s information functionality of a minimization principle induces multifractal–type Newtonian behaviors. The analysis of these behaviors through motion geodesics shows the fact that the center of the Newtonian-type multifractal force is different from the center of the multifractal trajectory. The measure of this difference is given by the eccentricity, which depends on the initial conditions. In such a context, the eccentricities’ geometry becomes, through the Cayley–Klein metric principle, the Lobachevsky plane geometry. Then, harmonic mappings between the usual space and the Lobachevsky plane in a Poincaré metric can become operational, a situation in which the Ernst potential of general relativity acquires a classical nature. Moreover, the Newtonian-type multifractal dynamics, perceived and described in a multifractal paradigm of motion, becomes a local manifestation of the gravitational field of general relativity.

DOUBLE STRUCTURES AND DOUBLE SYMMETRIES FOR THE EINSTEIN–KALB–RAMOND THEORY

We further study the two-dimensional reduced Einstein–Kalb–Ramond (EKR) theory in the axisymmetric case by using the so-called double-complex function method. We find a doubleness symmetry of this theory and exploit it so that some double-complex d×d matrix Ernst-like potential can be constructed, and the associated equations of motion can be extended into a double-complex matrix Ernst-like form. Then we give a double symmetry group [Formula: see text] for the EKR theory and verify that its action can be realized concisely by a double-complex matrix, form generalization of the fractional linear transformation on the Ernst potential. These results demonstrate that the theory under consideration possesses more and richer symmetry structures. Moreover, as an application, we obtain an infinite chain of double-solutions of the EKR theory showing that the double-complex method is more effective. Some of the results in this paper cannot be obtained by the usual (nondouble) scheme.

IWP SOLUTIONS FOR HETEROTIC STRING IN FIVE DIMENSIONS

We obtain extremal stationary solutions that generalize the Israel–Wilson–Perjés class for the low-energy limit of heterotic string theory with n≥ 3U(1) gauge fields toroidally compactified from five to three dimensions. A dyonic solution is obtained using the matrix Ernst potential (MEP) formulation and expressed in terms of a single real (3×3)-matrix harmonic function. By studying the asymptotic behavior of the field configurations, we define the physical charges of the field system. The extremality condition makes the charges saturate the Bogomol'nyi–Prasad–Sommmerfield (BPS) bound.

O(d, d)-Symmetry and Ernst Formulation of Einstein–Kalb–Ramond Theory

A Ernst-like matrix representation of (3+d)-dimensional Einstein–Kalb–Ramond theory is developed. The analogy with the Einstein and Einstein–Maxwell–Dilaton–Axion theories is discussed. The subsequent reduction to two dimensions is considered. It is shown that, in this case, the theory allows two different Ernst-like d×d-matrix formulations: the real nondualized target space, and the Hermitian dualized nontarget space one. The O(d, d)-symmetry is written in an SL (2,R) matrix-valued form in both cases. The Kramer–Neugebauer transformation, which algebraically maps the nondualized Ernst potential onto the dualized one, is presented.