I don't mean algebraic geometry and all that. I seek a no nonsense introduction to string theory in terms of algebraic quantum field theory.


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  • $\begingroup$ That is bound to be very difficult. It is hard enough to write basic conformal field theories in algebraic quantum field theory e.g. Wasserman. But for string worldsheet you will have to write down some more complicated CFT. And that is just a worldsheet theory without dealing with genus or moduli. $\endgroup$ – AHusain Apr 16 '17 at 23:28

String theory doesn't obey the axioms of algebraic quantum field theory and, sociologically speaking, string theorists do not think that algebraic quantum field theory is a promising path anywhere, so you won't find any credible texts on string theory based on algebraic quantum field theory.

The perturbative string theory calculations are based on two-dimensional conformal field theories and they allow calculations of the "bootstrap" type and for similar reasons, the situation may be considered analogous to algebraic quantum field theory, too. But the precise formalism promoted by the actual champions of algebraic quantum field theory isn't usable in string theory.

It isn't really usable in modern quantum field theory, either. The logic behind the existence of divergences etc. was really revised in the 1970s. Algebraic quantum field theory was an older attempt than the Renormalization Group of the 1970s and it was realized that it was incorrect on many important assumptions.

  • $\begingroup$ I am sorry but the paper is in no sense "recent" - the digits 95 in the URL indicate that it is from the year 1995, i.e. 22 years ago. Second, the paper is below 50 citations according to SPIRES and except for one vague reference by Giddings, none of those are from people who are actually string theory experts. I wrote about the incompatibility of Buchholz and string theory e.g. in 2006, see motls.blogspot.com/2006/04/… , after I talked to him for hours. $\endgroup$ – Luboš Motl Jun 17 '17 at 7:19

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