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Fermionic determinant for dyons and instantons with nontrivial holonomy

Nikolay Gromov·Sergey Slizovskiy
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Abstract

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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Nikolay Gromov, Sergey Slizovskiy. 2005-08-04. Fermionic determinant for dyons and instantons with nontrivial holonomy. https://doi.org/10.1103/physrevd.71.125019

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