Motivated by the (for me very useful) remark ''Standard model generations in string theory are the Euler number of the Calabi Yau, and it is actually reasonably doable to get 4,6,8, or 3 generations'' in https://physics.stackexchange.com/a/22759/7924 , I'd like to ask:

Is there a source giving this sort of dictionary how to relate as much as possible from general relativity and the standard model to string theory, without being bogged down by formalism, speculation, or diluted explanations for laymen?

Or, if there is no such dictionary, I'd like to get as answers contributions to such a concise dictionary.

[Edit April 30, 2012:] I found some more pieces of the wanted dictionary in http://www.physicsforums.com/showthread.php?p=3263502#post3263502 : ''branes and extra dimensions have proved to be implicit in standard quantum field theory, where they emerge from the existence of a continuous degeneracy of ground states. That multidimensional moduli space of ground states is where the extra dimensions come from, in this case! Branes are domain walls separating regions in different ground states, strings are lines of flux connecting these domain walls. Furthermore, in gauge theories with a small number of colors, it looks like the extra dimensions will be a noncommutative geometry, it's only in the "large N" limit of many colors that you get ordinary space.''

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    $\begingroup$ It's a good question, unfortunately, the dictionary starts and ends at the Euler number. Further, Vafa has alternate ways of embedding the standard model using branes, in a different string theory, but it is not clear it is as phenomenologically successful. Vafa's methods allow for natural "little hierarchy" where the electron is light and the CKM matrix is naturally nearly diagonal, but they aren't as natural as Witten-style E8 models IMO. The dictionary is different in Vafa brane models. Getting a near-diagonal CKM is a good stringent test of geometry, but it needs methods beyond topology. $\endgroup$
    – Ron Maimon
    Commented Apr 14, 2012 at 16:12
  • $\begingroup$ @RonMaimon: I thought the dictionary would contain at least items such as a simple reason for the existence of a massless graviton.... $\endgroup$ Commented Apr 16, 2012 at 17:10
  • $\begingroup$ I don't know how you make a massive graviton in string theory. The reason is the gravitational ward identity--- this enforces the quantum version of general covariance (in S-matrix, i.e. massless graviton). The general covariance is derived from exponentiating world sheet insertions in an early chapter of Greene/Schwarz/Witten, this is the reason for massless graviton. The gauge groups, however, are either brane-stacks (Vafa-style) or heterotic E8 with a flux embedding of the compactification holonomy (E8 magnetic fields threading the compactification), and this produces E6 GUT (SO(10)->SM). $\endgroup$
    – Ron Maimon
    Commented Apr 16, 2012 at 17:59
  • $\begingroup$ The dictionary is annoying--- you get a gravitino in Witten style compactifications, and SUSY, and you need to understand SUSY breaking, and this is more difficult to do. I also didn't read more than a small fraction of the model-building literature, so I am not in the best position to give a comprehensive answer. Lubos might, but I think the best bet is someone older, who read the 80s stuff--- there are a lot of dormant ideas from the 80s. $\endgroup$
    – Ron Maimon
    Commented Apr 16, 2012 at 18:00
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    $\begingroup$ "A dictionary" is a big word - it suggests many entries in it, with a clear enough definition what may count as an entry and what doesn't. I don't see any other "entries of the very same kind" to the counting of the generations and/or Euler characteristic. There are many other things that may be "translated" between two languages but which two languages and which classes of "words" do you want to be translated by the dictionary? Most of the translations I can think of are of very different character than this very special insight about the generations in heterotic string theory. $\endgroup$ Commented Jan 30, 2014 at 14:10

1 Answer 1


There is a mathematically precise dictionary from perturbative string theory to perturbative quantum field theory obtained by systematically taking the point particle limit of string backgrounds encoded by 2d SCFTs via a "degeneration limit" that turns these into spectral triples.

I have written an exposition of this process, with pointers to the literature, at PhyiscsForums, here:

Spectral Standard Model and String Compactifications

(Beware though that, while precise, there is much, much room to develop and explore the mathematical process further. )


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