Nonabelian duality and analytic continuation of instantons

TL;DR

This paper explores an extension of the instanton ansatz within a gauge theory framework, revealing new duality properties and a connection to complex-analytic functions through the inclusion of the Levi-Civita tensor.

Contribution

It introduces a novel extension of the instanton ansatz incorporating the Levi-Civita tensor, leading to new duality properties and complex-analytic solutions.

Findings

Discovery of a new duality in gauge theories.

Selfduality condition linked to complex-analytic functions.

Extension of the instanton ansatz with Levi-Civita tensor.

Abstract

Within the framework of the gauge O(1,3)\times O(1,3)-theory, an extension of the Belavin-Polyakov-Schwarz-Tyupkin ansatz is proposed by incorporation there the Levi-Civita tensor. The duality properties of the theory, admitting introduction the complex structure, are such that selfduality condition of the field tensor is an equation for complex-analytic function. New type of duality is found out.