SU(N) caloron measure and its relation to instantons

Details SU(N) caloron measure and its relation to instantons SU(N) caloron measure and its relation to instantons

2005-02-15

arxiv.org/abs/hep-th/0502132v2

Phys.Rev. D72 (2005) 025003

Physics

High Energy Physics

High Energy Physics - Theory

15 p

Scientific paper

10.1103/PhysRevD.72.025003

Calorons of the SU(N) gauge group with non-trivial holonomy, i.e. periodic instantons with arbitrary eigenvalues of the Polyakov line at spatial infinity, can be viewed as composed of N Bogomolnyi--Prasad--Sommerfeld (BPS) monopoles or dyons. Using the metric of the caloron moduli space found previously we compute the integration measure over caloron collective coordinates in terms of the constituent monopole positions and their U(1) phases. In the limit of small separations between dyons and/or trivial holonomy, calorons reduce locally to the standard instantons whose traditional collective coordinates are the instanton center, size and orientation in the color space. We show that in this limit the instanton collective coordinates can be explicitly written through dyons positions and phases, and that the N-dyon measure coincides exactly with the standard instanton one.

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