Sleipnir - Manga
Summary
From MangaHelpers:
"The Sixth Dimension Experiment." This experiment, in attempting to open one of the eleven dimensions in our reality, the sixth dimension (Secht), resulted in a catastrophic explosion that killed 110 million people and left 12 countries in ruins. The originator of this experiment, Himeka Yuki, bearing the total responsibility for the failure of this experiment, has been banished from reality for eternity. In response to this event, the world leaders in sciences formed a monitoring agency known as "Zeien" to keep control of all scientists and technology in order to prevent another Sixth Dimension Experiment.
10 years have passed since the incident. Takaomi Yuki, the younger brother of Himeka, notices a change in the "Time Machine Destination" that his sister has given him before her banishment. Suddenly, the device summons a lively girl armored with metals he has never seen. "Takaomi-san! To save Earth, pull out your lance and ride me!" To uncover the truth, the two will begin an adventure that crosses time and space. [DrCoke]
In a system like that there would need to be rigorous documentation and certificates of prior ownership/guardianship or else anyone and everyone would just get grabbed off the street and enslaved at any time, and such a society would collapse instantly. So these slavers wouldn't have such documentation unless it was a forgery since the kids were just kidnapped; both offenses should be very serious capitol crimes. Once again, the day is saved by glorious Bureaucracy! (and the MC's knowledge and exploitation there of).