Fermionic determinant for dyons and instantons with nontrivial holonomy

Details Fermionic determinant for dyons and instantons with nontrivial holonomy Fermionic determinant for dyons and instantons with nontrivial holonomy

2005-04-04

arxiv.org/abs/hep-th/0504024v2

Phys.Rev. D71 (2005) 125019

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, published version, references added

Scientific paper

10.1103/PhysRevD.71.125019

We calculate exactly the functional determinant for fermions in fundamental representation of SU(2) in the background of periodic instanton with non-trivial value of the Polyakov line at spatial infinity. The determinant depends on the value of the holonomy v, the temperature, and the parameter r_12, which at large values can be treated as separation between the Bogomolny--Prasad--Sommerfeld monopoles (or dyons) which constitute the periodic instanton. We find a compact expression for small and large r_12 and compute the determinant numerically for arbitrary r_12 and v.

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