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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 extreemly short and doesn't cover alot sadly.

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")

Thanks!

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Costello's recent book on renormalization does some of this for QFT, though it's somewhat light on the physical aspects of the subject. –  Moosbrugger Aug 2 '11 at 20:03
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I'm afraid the best we might dream of can only be in the "Definition-Claimed Theorem-No proof" style :p –  Yuji Tachikawa Aug 3 '11 at 7:51
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@Yuji: I echo the sentiment. Often I would already be happy with a definition! –  José Figueroa-O'Farrill Aug 3 '11 at 21:25
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6 Answers 6

up vote 20 down vote accepted

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: http://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!)

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You can link to the original site of the activity, where you can grab the notes for free: math.ias.edu/node/96 That is perhaps more truly gauche :) –  José Figueroa-O'Farrill Aug 2 '11 at 19:23
    
+1 Thanks, that book does indeed look very promising. I'll probably get this to review on QFT. Judging from the José's link however, the String Theory part doesn't seem to follow this rigor as was started in the QFT part. It seems to drift of into a the standard physics approach instead of a more mathematical one. @Jon, do you own a copy? Would you say this holds true for the printed version? I'll try getting my hands on one as soon as i can –  Michael Kissner Aug 2 '11 at 19:42
    
The published version differs significantly from the electronic notes. Here are the complete scans of both books: gen.lib.rus.ec/… –  Dmitri Pavlov Aug 3 '11 at 9:01
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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.

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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.

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Authors of those books? –  Qfwfq Aug 2 '11 at 22:44
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I think rigorious string theory is just that what mathematicians make out of it when they got inspired.

If you had a course in classcial 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 expalaining Gauged Linear Sigma model, SCFTs etc. ()You find this stuff also in "Mirror Symmetry").

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What about "String Theory and M-Theory: A Modern Introduction"?

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I don't think that BBS falls into the category of "mathematically rigorous". It's a very good, intuitive book. –  Dimensio1n0 Nov 8 '13 at 4:17
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http://superstringtheory.com ....this website might help you.

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I'm sorry, but that site is meant as a popular introduction to the subject. –  Michael Kissner Aug 2 '11 at 18:59
    
I had found there papers by Witten; 1: overview of k-theory applied to string theory 2: String Theory and Noncommutative Geometry –  asche Aug 3 '11 at 16:11
    
@MichaelKissner: Well, popular + semi-popular, to be precise (it has a semi-popular option). –  Dimensio1n0 Sep 17 '13 at 13:47
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