Towards a Coulomb gas of instantons in the SO(4)xU(1) Higgs model on R_4

TL;DR

This paper extends the SO(4)×U(1) Higgs model on four-dimensional space by adding an F^3 term, analyzing multi-instanton interactions and their mathematical structure, with detailed numerical studies of single-instanton solutions.

Contribution

It introduces a modified Higgs model with a new interaction term and explores the resulting instanton configurations and their interactions in detail.

Findings

Action includes nontrivial multi-instanton interactions

Expresses the action as the inverse Laplacian on R4

Numerical analysis of one-instanton solutions

Abstract

The $SO(4)\times U(1)$ Higgs model on $\R_4$ is extended by a $F^3$ term so that the action receives a nonvanishing contribution from the interactions of 2-instantons and 3-instantons, and can be expressed as the inverse of the Laplacian on $\R_4$ in terms of the mutual distances of the instantons. The one-instanton solutions of both the basic and the extended models have been studied in detail numerically.