Book on mathematical "rigorous" String Theory? 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")
 A: The mathematical aspects of string theory are wide-ranging, so I think looking for a mathematically rigorous treatment of the construction of string theories basically leads you to consider studying the output of a whole industry of mathematical physics research within algebraic geometry, representation theory, k-theory, differential topology, etc. There are a few mathematical books, e.g.:


*

*Enumerative Invariants in Algebraic Geometry and String Theory [Abramovich, D. et al];

*Orbifolds and Stringy Topology [Adem, A. et al];

*String Topology and Cyclic Homology [Cohen, R.L. et al];

*Strings and Geometry [Douglas, M. et al];

*Mathematical Aspects of String Theory [Yau, S.-T.];

*Supersymmetry for Mathematicians - An Introduction [Ramachandran, V.S.];

*Supersymmetry and Supergravity [Wess + Bagger];

*Mirror Symmetry [Hori, K. et al];

*Mirror Symmetry and Algebraic Geometry [Cox, D.A. + Katz, S.]; 

*Homological Mirror Symmetry - New Developments and Perspectives [Kapustin, A. et al]; etc.


Best intro would be, as pointed out previously, Quantum Fields and Strings.
A: There is the two volume set Quantum Fields and Strings: A Course for Mathematicians that attempts to bridge the gap. Here's an Amazon link: https://www.amazon.com/Quantum-Fields-Strings-Course-Mathematicians/dp/0821820141.
(If it is gauche to give an Amazon link, please change my post, o moderators!)
A: There is the currently in-press book "Mathematical Foundations of Quantum Field and Perturbative String Theory" (n-cafe,nLab) edited by Schreiber and Sati and published in the AMS series Proceedings of Symposia in Pure Mathematics.
Links to arXiv copies of contributions are available at the above linked nLab page.
A: What about "String Theory and M-Theory: A Modern Introduction"?
A: I think rigorous string theory is just that what mathematicians make out of it when they got inspired.
If you had a course in classical mechanics and have seen a Lagrangian and calculated a Gaussian integral once in your live you already know a lot about physics.
To get an insight into path integral calculations there is the great book "Mirror Symmetry" by Aspinwall, Klemm, Hori et al. It is split in physics and mathematics parts. (The mathematics does not define virtual fundamental class.)
Then there is the newer book called "Dirichlet branes and mirror symmetry". Here mathematics and physics are taught closer together.
A book on Gromow-Witten theory is "Mirror symmetry and algebraic geometry". It also contains an appendix explaining Gauged Linear Sigma model, SCFTs etc. ()You find this stuff also in "Mirror Symmetry").
A: http://superstringtheory.com
....this website might help you.
