# A dictionary of string - standard physics correspondences

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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 http://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.''

This post imported from StackExchange Physics at 2014-04-18 15:57 (UCT), posted by SE-user Arnold Neumaier

recategorized Apr 20, 2014
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.

This post imported from StackExchange Physics at 2014-04-18 15:57 (UCT), posted by SE-user Ron Maimon
@RonMaimon: I thought the dictionary would contain at least items such as a simple reason for the existence of a massless graviton....

This post imported from StackExchange Physics at 2014-04-18 15:57 (UCT), posted by SE-user Arnold Neumaier
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).

This post imported from StackExchange Physics at 2014-04-18 15:57 (UCT), posted by SE-user Ron Maimon
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.

This post imported from StackExchange Physics at 2014-04-18 15:57 (UCT), posted by SE-user Ron Maimon
"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.

This post imported from StackExchange Physics at 2014-04-18 15:57 (UCT), posted by SE-user Luboš Motl
@LubošMotl: When I asked the question I thought there might be many entries. So I was disappointed of the answer. I want to know what of string theory can be understood on an intuitive but still technical level, with a background in general relativity, quantum fields and conformal fields, but without background knowledge from string theory.

This post imported from StackExchange Physics at 2014-04-18 15:57 (UCT), posted by SE-user Arnold Neumaier
Dear @ArnoldNeumaier, I don't really claim that there are no other entries that you could consider analogous. I just think that it's not clear which entries you would consider analogous and which entries you would not. For example, there is F-theory model building where you can link the gauge group in the spacetime (like E6) with the type of singular fibers in the F-theory. Is that analogous to the counting of generations in heterotic string theory? If it is, we may be forced to include almost every insight/sentence about string phenomenology in thousands of papers, too. ;-)

This post imported from StackExchange Physics at 2014-04-18 15:57 (UCT), posted by SE-user Luboš Motl

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You are asking for an introductory survey of what is called string phenomenology

First a reference, then some comments:

One book collection which goes at least a long way towards providing a survey of which aspects of string theory map to which aspects of the standard model in the low energy effective theory is this here:

(Let me know if you don't know how to get an electronic copy from this data...)

In there, the lectures closest to being dictionary-like are probably these courses:

• Course 1:  Topics in string phenomenology by Antoniadis
• Course 2:  Orientifolds, and the search for the Standard Model in string theory by Kiritsis
• Course 7: The standard model from D-branes in string theory by Uranga
• Course 12: Lectures on constructing string vacua by Denef

Now the comment:  there are MANY ways in which quantum field theory arises inside string theory. String theory is like a huge dictionary of QFTs mapping out a large part of their moduli space, and connecting them in ways ("dualities", "geometric engineering") which are non-obvious from the point of view of just QFT. String theory is to QFT as complex analysis is to real analysis: a larger space in which all the relations in the smaller space become manifest.

In particular there are many different ways for string model building. The relation between CY Euler characteristic and SM generations in the above question arises only in one class of them, namely in the traditional heterotic model building. This is the class of string models with the longest history.

But in recent years other classes have found much attention, notably models of intersecting branes in type II. Here the "dictionary" is a very different one, but is very beautiful, too: all the properties of the standard model are encoded in the precise geometry of intersecting branes with open strings on them.

Then there is M-theory model building and more. Of course all these are related by duality.

And one well-kept truth is the following: this huge collection of models that have been discussed in the literature is certainly just the tip of the iceberg, this is just what is easiest to describe!

In particular, the bulk of model building in existing literature works and argues with fairly classical geometry, with string sigma-models built from differential geometric target spaces.

But abstractly a perturbative string vacuum is any 2d SCFT of central charge 15. "Most" of these will not be geometric at all, at least not in the compact dimensions. Very very little has been studied of this large moduli space of 2d SCFTs. All of the models currently under discussion may be too naive simply because they start geometrically.

To amplify this: there is a systematic way to take the point particle limit of a 2d SCFT  (see the reference here ) and the result is... a spectral triple.  Abstractly speaking, that relation is the "true dictionary" between string theory and point particle QFT. And spectral triples, as you know, generically do not describe "geoemtric" backgrounds, that's their whole point.

answered Apr 18, 2014 by (6,095 points)
edited Apr 18, 2014

author: Douglas author:Kiritsis  String theory and the real world

indeed does not give any hit in scholar.google.com.

It's on GoogleBooks. And elsewhere... Send me an email if you get stuck.

Thanks; found it in our library. How would you suggest to begin reading? I know much about QFT and CFT but hardly anything about string theory.

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I will put down some such correspondences here that I recall, and expand on it slowly. I haven't explained anything here, and have instead linked to explanations.

• The distance between D-branes and the Higgs (explanation)
• The winding number and the electric charge (explanation)
• The worldsheet fermions and the spin (explanation)
• The Calabi-Yau Euler Number and the Standard Model generations (explanation)
• The open bosonic strings and the gauge bosons (explanation)
• The closed bosonic strings and the gravitons (explanation)
• The graviton field and the spacetime metric (minus minkowski) (explanation)
• The dilaton and the radion (explanation) [1]
• The string casimir energy equation and the casimir energy (explanation)
• The string mass spectrum and the particle masses (explanation)
• The classical effective gravitational polyakov action and the EH action  (explanation)

[1] Not exactly a string-standard_physics correspondence, but more of a string-kaluza_klein correspondence.

I can't think of any more at the moment, but will expand this answer each time I recall something.

There is the correspondence between the 10 dimensions of string theory and the 5 dimensions of Kaluza-Klein that has to do with the dimensions of a manifold with $U(1)\times SU(2)\times SU(3)$symmetry, but this is more direct, because SUGRA is an extension of Kaluza-Klein theory, so I'll leave it out.

### Reply to Arnold Neumaier's comment

• open stringgauge theory
• closed stringgravity

mentioned in Urs Schreiber's comment. This can be seen just by looking at the massless fields of, for example, Type I Superstring Theory. This is how the spectrum looks like:

 Sector Spectrum Massless Fields RR $\mathbf{8}_s\times\mathbf{8}_s$ $A_1$ RNS $\mathbf{8}_s\times\mathbf{8}_v$ $\Psi_\mu$ NSR $\mathbf{8}_v\times\mathbf{8}_s$ $\lambda'$ NSNS $\mathbf{8}_v\times\mathbf{8}_v$ $g_{\mu\nu}, \Phi$ R $\mathbf{8}_s$ $Y_{\mu\nu}, H_{\mu\nu}$ NS $\mathbf{8}_v$ $F_{\mu\nu}, G_{\mu\nu}$

As you can see, the photino, gluino, photon, and gluon (Y, H, F, and G) are all in the open string sectors (those that do not involve tensoring of states or products of $\mathbf{8}_s , \mathbf{8}_v$. These are of course the gauge fields, whereas the metric tensor, or the graviton (g) and the dilaton field (Φ), and their superpartners, the gravitino and the dilatino  (Ψ and λ), and the Ramond-Ramond field, are all found in the closed string sectors.

answered Apr 18, 2014 by (1,985 points)
edited Dec 12, 2015

The dictionary starts with the paramount entry:

"open string $\leftrightarrow$ gauge theory; closed string $\leftrightarrow$ gravity".

The rest is details ;-)

nice format of answering this. I am looking forward to more entries!

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