What does Touma say to the "Replica" Sorcerer with the Obsidian Blade?
Manga volume 11, chapter 64, page 15


The full quote was: 


  "That’s right, it's a promise. This promise is to protect Misaka Mikoto and the world around her. This is my agreement with a certain nameless person who fell in love with her so quickly."


He explains this to Shirai Kuroko regarding his promise with Etzali from Toaru Majutsu no Index Light Novel Volume 08. 

source: Touma's quotes on Toaru Majutsu no Index Wikia