Cardfight!! Vanguard Gaiden: If Cardfight!! Vanguard Extra Story -if-
Kouji Ibuki is a Vanguard Fighter. One day, Ibuki was called out to the Tatsunagi residence, when he was suddenly transported to the -IF- world. But the -IF- world has a distorted history, where cardfighting doesn't exist!?
In the -IF- world, Ibuki met with some mysterious girls. The magical girl Emi Sendou, and the fairy of the cards Shuka. They are the "Blaster Pair" that summons units from cards in their battle against the evil minions of Jammer!
And so the quartet of Ibuki, Emi, Shuka, and Suiko Tatsunagi who was caught up in the situation, begin their journey to recover the true history.
[Source: Cardfight!! Vanguard Wiki]