# Advanced topics in string theory

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I'm looking for texts about topics in string theory that are "advanced" in the sense that they go beyond perturbative string theory. Specifically I'm interested in

1. String field theory (including superstrings and closed strings)
2. D-branes and other branes (like the NS5)
3. Dualities
4. M-theory
6. Matrix theory
7. F-theory
8. Topological string theory
9. Little string theory

I'm not interested (at the moment) at string phenomenology and cosmology

I prefer texts which are (in this order of importance)

• Top-down i.e. would give the conceptual reason for something first instead of presenting it as an ad-hoc construction, even if the conceptual reason is complicated
• Use the most appropriate mathematical language / abstractions (I'm not afraid of highbrow mathematics)
• Up to date with recent developments

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edited Apr 20, 2014

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Among normal books, Becker-Becker-Schwarz probably matches your summary most closely. However, you may want to look at a list of string theory books:

http://motls.blogspot.com/2006/11/string-theory-textbooks.html

Don't miss the "resource letter" linked at the bottom which is good for more specialized issues such as string field theory. An OK review of string field theory could be this one

http://arxiv.org/abs/hep-th/0102085

but it was written before many recent advances, such as Martin Schnabl's analytic solution for the closed string vacuum and its followups.

I must correct your comment that you're interested in "nonperturbative" issues such as string field theory. It's been established that despite some expectations, string field theory is just another way to formulate perturbative string theory. It is not useful to learn anything about the strong coupling, not even in principle. And it becomes a mess in the superstring case. There are no functional string field theory descriptions with closed string physical states seen in the physical spectrum at all; it has various reasons. For example, a description that is ultimately "a form of field theory" can never produce the modular invariance $SL(2,{\mathbb Z})$ (needed to get rid of the multiple counting of the 1-loop diagrams). String theory is extremely close to a field theory but it is not really a field theory in spacetime in this strict sense and this fact becomes much more apparent for closed strings (which include gravity at low energies) than in the case of open strings (that may be largely emulated by point-particle fields – related to Yang-Mills being in the low-energy limit of open strings).

For a review of topological string theory, see e.g.

http://motls.blogspot.com/2004/10/topological-string-theory.html

Quite generally, when you study the literature (or reviews), you may find out that your pre-existing expectations about the amount of knowledge people have about various subtopics i.e. about their "relative importance in the current picture" is different than you may expect a priori. Without knowing the actual content, one can't sensibly "allocate" the number of pages to various subtopics as you did so.

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answered Jan 7, 2012 by (10,278 points)
Thx a dozen for the answer! Regarding string field theory, I still have a feeling I need to learn because many string theory texts allude to it even if not using it. At the least I want to understand why it ultimately failed. Also it might be that some ideas from SFT can be recycled in some ultimately more successful way. Besides that, my understanding is that SFT did have at least 1 success namely Sen's work about D-brane annihilation

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Regarding BBS, I have it (made it to page 189) but I got the feeling it glosses over too many things. I found D'Hoker's text in "Quantum Fields and Strings: A Course for Mathematicians vol. 2" much more readable, even though it might be partly an illusion because my mind was prepared by other texts. Unfortunatelly, though, D'Hoker doesn't go beyond basic perturbation theory

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Dear @Squark, thanks for your interest. SFT didn't really "fail". It is a totally consistent and from many viewpoints uniquely useful - "explicitly local, off-shell" - formulation of perturbative open string dynamics and the open-string-related solutions such as D-branes solutions (as tachyon condensation from other D-brane starting points). The most explicit and rigorous framework to discuss tachyon condensation etc. It's very manageable in the bosonic string case. People could have expected some other miraculous things from SFT but there have never been "rational justifications" for them.

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Otherwise I skipped F-theory, Matrix theory, and little string theory. There are specialized reviews of those because they're really special. To understand F-theory including the applications that give it the "juice", one must understand lots of algebraic geometry, bundles, and so on. A great arena for people who love (advanced) geometry. The physical essence is really simple: it's type IIB where the axion-dilaton $\tau$ is interpreted as the complex structure of a $T^2$ fiber of two new dimensions attached to each point.

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Matrix string theory was reviewed in various papers e.g. Susskind-Bigatti and Taylor, see the resource letter by Marolf at the bottom of my 2006 page. Little string theory is extremely special. One should read the original papers and their most important followups. This is a domain intensely studied by a few people in the world so it's obviously not terribly efficient to write "textbooks" of it.

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And one more comment. I still feel that you underestimate the perturbative part of the theory. In the mid 1990s, there's been a huge activity that ultimately clarified many features of the non-perturbative behavior of string theory. But it's still true that most of the phenomena are accessible from one perturbative description or another - dualities are just statements of equivalences (sometimes nonperturbative equivalences) between different descriptions that were known perturbatively. But much of the "explicit" quantitative calculation has to use *some* expansions.

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You can consult this webstie.

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answered Jan 7, 2012 by (345 points)
This URL was (for years) on the top of my page, too. ;-)

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Sorry, I did not check your link. But let this post be as it is.

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