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

Abstract

The $SO(4)\times U(1)$ Higgs model on ${\mathbb{R}}_4$ 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 ${\mathbb{R}}_4$ 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.

29 pages LaTeX, 4 Figures available from authors on request

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