Dreamland with classic Higgs field, dimensional reduction and all that

This text, on the one hand, is related to the talk delivered at the conference “Gauge Fields. Yesterday, Today, Tomorrow” dedicated to the 70th anniversary of Andrei Slavnov; on the other – in the form of a fairy tale – it summarizes some results of the research performed after this Fest, mainly due to discussion around the talk.

Received in December 2010