Elsevier

Nuclear Physics B

Volume 248, Issue 1, 17 December 1984, Pages 209-252
Nuclear Physics B

Spherically and axially symmetric SU(N) instation chains with monopole limits

https://doi.org/10.1016/0550-3213(84)90594-7Get rights and content

Abstract

Spherically and axially symmetric sequences of SU(N) instantons (i.e. with action densities depending on t, r, and t, r, θ respectively) are studied such that static monopoles with corresponding symmetries (with energy densities depending on r and r, θ respectively) are obtained trivially in a scaling limit. Static techniques are used to construct finite action selfdual solutions through a trick introduced in previous papers. Spherically symmetric solutions are obtained from an ansatz for the gauge potentials. Axially symmetric ones are studied through the construction of super-potentials in the context of Lax pair formalism. Spherical symmetry is obtained once again as special cases in this, more general, context. The formalism is given for arbitrary N. SU(2) examples are compared to those presented in previous papers. Explicit SU(3) examples are constructed. The motivations and the basic ideas are discussed in detail in the introduction. The relation of each part with the works of other authors are pointed out.

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