Monopole solutions to the Bogomolny equation as three-dimensional generalizations of the Kronecker series

Abstract

The Dirac monopole on a three-dimensional torus is considered as a solution to the Bogomolny equation with non-trivial boundary conditions. The analytical continuation of the obtained solution is shown to be a three-dimensional generalization of the Kronecker series. It satisfies the corresponding functional equation and is invariant under modular transformations.

13 pages, 1 figure

References in corpus (3)

• Characteristic Classes and Integrable Systems for Simple Lie Groups
• Characteristic Classes and Integrable Systems. General Construction
• Monopoles and Modifications of Bundles over Elliptic Curves

Cited by in corpus (3)

• Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices
• Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles
• Qubits and STU Black Holes with Eight Electric and Magnetic Charges