I've been looking high and low for a mathematical book on String Theory. The only book I could find was "A Mathematical Introduction to String Theory" by Albeverio, Jost, Paycha and Scarlatti. I only stumbled upon this because I really like Jost's other books.
After reading it, I found myself craving more. However, the above book is extremely short, and sadly doesn't cover a lot.
I've been having trouble reading the current textbooks on String Theory. To me, it often seems that certain mathematical concepts are simply applied without checking or reasoning, something that has been bugging me ever since studying QFT. As I'm not a physicist, it's rather likely that I'm still lacking the intuition to see these things.
My question is, are there any other introductory books/review-articles on String Theory written in a more mathematically rigorous way? By this I mean, books that are written in the style of a common math book? ("Definition-Theorem-Proof-Style")