Self-Dual Connections and the Equations of Fundamental Fields in a Weyl-Cartan Space

TL;DR

This paper explores a special Weyl-Cartan space with torsion, revealing self-duality in curvature and gauge fields, and derives general solutions showing string-like singularities and algebraic string dynamics.

Contribution

It introduces a novel geometric framework with self-dual connections and derives explicit solutions with string-like singularities.

Findings

Self-duality of curvature and gauge fields in Weyl-Cartan space

Explicit general solutions with string-like singularities

Algebraic dynamics of a string system from the solutions

Abstract

Spaces with a Weyl-type connection and torsion of a special type induced by the structure of the differentiability conditions in the algebra of complex quaternions are considered. The consistency of these conditions implies the self-duality of curvature. The Maxwell and SL(2, C) Yang-Mills fields associated with the irreducible components of the connection also turn out to be self-dual, so that the corresponding equations are fulfilled on the solutions of the generating system. Using the twistor structure of the latter, its general solution is obtained. The singular locus has a string-like (particle-like) structure and generates the self-consistent algebraic dynamics of the string system.