where η η ¯ ¯ μ μ ν ν a is the anti- 't Hooft symbol, r is the distance from the point x to the center of the caloron, ρ is the size of the caloron, τ τ is the Euclidean time and T is the temperature. This solution was found based on a periodic multi-instanton solution first suggested by 't Hooft and published by Witten.