Types of quantum field thories
Broadly speaking, string phenomenology refers to investigations of the connection of string theory to experimentally observed physics. More restrictively it refers to constructions of string theory vacua whose effective field theory reproduces the standard model of particle physics and/or the standard model of cosmology.
String theory models natually match the general conceptual structure of the standard model of particle physics plus gravity (which is what drives the interest in string theory in the first place): for instance the standard model is a four dimensional QFT with a non-Abelian gauge symmetry, several families of chiral fermions and hierarchical Yukawa couplings – and the same is true for the generic compactification of the effective QFT that describes heterotic string theory on a 6-dimensional compact space (CHSW85) as well as for 11-dimensional supergravity/M-theory compactified on a G2-manifold (AW01).
This structure alone already implies a variety of 3-body decays of the heavier fermions into the lighter ones and the existence of massive vector bosons coupling to charged currents, which in the observed standard model of particle physics are the W-boson, etc. (See section III of AKK12 for an exposition.)
Therefore it is not hard to find string theory compactifications that resemble the observed particle physics in broad strokes. Under some simplifying assumptions many string models have been built that very closely resemble also the fine-structure of the standard model.
A central technical issue with string model building is that of the Kaluza-Klein mechanism involved: the moduli stabilization. Historically there had been the hope that the consistency condition of moduli stabilization on string models is so strong that it strongly reduces the number of models that look like the standard model. Arguments that the number is still “not small” even with various extra assumptions lead to the term of a landscape (moduli space) of string theory models, which remains, however, poorly understood. Arguments for properties of low-energy effective QFTs that rule out a possibe string-theoretic model have been brought forward for instance in (Vafa05). A review of what is known about the space of possibilities is in (Taylor11).
While all this remains poorly understood, a noteworthy difference of string phenomenology to model building in bare QFT is that a) there is a larger framework at all in which to search for models and b) with every model automatically comes a UV-completion, which is the basic motivation for embedding the standard model of particle physics in a broader theory of quantum gravity in the first place.
A good account of what it means to have a realistic string theory model and what the subtleties are, and in which sense they have already been found abundantly or not at all, is in the introduction of (Dolan-Krippendorf-Quevedo).
Since a realistic string theoretic model is, by desing, a unification of the standard model of particle physics with quantum gravity aspects and hence at least with aspects of the standard model of cosmology, there are more constraints on such a model than are usually imposed on model building in particle physics alone: the model is not only supposed to reproduce the fundamental particle content but also address moduli stabilization, the cosmological constant and dark matter (see e.g. Dolan-Krippendorf-Quevedo 11, p. 3).
Accordingly one strategy to build models is to first aim for the correct fundamental particle content, and then incrementally adjust to account for the global gravitational constraints. For instance in type II intersecting brane models people often consider just an open neighbourhood of a singular point in a KK-compactification space, adjust the model there, and then later ask about embedding this local construction into an actually globally defined compactification space (typically a Calabi-Yau manifold for compactifications aiming for low energy supersymmetry in the effective 4d model).
This approach is known as the bottom-up approach to string model building (AIQU 00).
Examples of models in string phenomenology include
See at References - Models below.
The models in heterotic string theory follow the historically original and hence oldest strategy of finding semi-realitsic GUT models in string theory (see (Witten 02) for a brief list of motivations for these models): one considers a Kaluza-Klein compactification of heterotic string theory/heterotic supergravity on a closed manifold of dimension 6 with a non-trivial gauge field configuration on it. By choosing different values of the holonomy of this gauge field around non-trivial singular 1-cycles in the compact space (usually referred to as “Wilson lines” in this context) one obtains different effective physics in the remainind 4-dimensional space.
Since most of string model building was aimed for reproducing the minimally supersymmetric exension of the standard model of particle physics, these approaches usually take that compact 6-manifold to be a complex 3-dimensional Calabi-Yau manifold.
More in detail, the paradigm of this approach compactification of the E8 E8 heterotic string theory on a Calabi-Yau manifold Euler characteristic , leading to a three-generation E6-model. Further gauge spontaneous symmetry breaking may be achieved e.g. by the addition of Wilson lines and a final breakdown of , supersymmetry is assumed to take place due to some field-theoretical non-perturbative effects.
In contrast to the construction of “heterotic standard models” above, which are basically plain variants of the old Kaluza-Klein compactification mechanism where the effective gauge fields in 4-dimensional spacetime arise as components of the field of gravity in higher dimensions, in type II string theory with D-branes there are open strings whose massless excitations yield gauge fields “directly”. The precise nature of these gauge fields and their couplings depends on the precise boundary conditions of these open strings, hence on the choice of D-branes that they end on.
Therefore in what are called “intersecting D-brane models” one considers Kaluza-Klein compactifications of type II string theory with D-branes that intersect in an intricate pattern in the compactification space. By choosing this intersection geometry suitably, one obtains various different realizations of gauge theory in the effective 4-dimensional physics.
One way to neatly reorganize the required data for such type II compactifications is to formulate them in terms of “F-theory”, which is why some of this type II model building now goes by names like “F-theory phenomenology” or similar.
The moduli stabilization in these type of models can be achieved by choosing the various RR-field and B-field field strength (the “fluxes”) on the compactification space such that its curvature forms have certain specified periods on non-trivial singular cycles of the compactification space. See (Denef 08) for introduction and review of such type IIB flux compactification.
Since there are only finitely many – but many – such choices, it is in this context that people first tried to count the number of possibilities of building models (under all these assumptions, though) and found these large finite numbers such as the meanwhile proverbial number (coming from an estimate of the number of non-tivial cycles in a generic Calabi-Yau and the number of choices of periods of the “flux” fields) which then led them to speak of the “landscape of string theory vacua”. (Which of course without making a bunch of assumptions is vastly bigger, even.)
Due to the relation between supersymmetry and Calabi-Yau manifolds, of particular interest is the case of F/M-theory on elliptically fibered Calabi-Yau 4-folds, see there for more.
For references see below at References - Models in type II string theory
Another approach is to start with 11-dimensional supergravity with some of its “M-theory”-corrections taken into account and then apply Kaluza-Klein compactification in that context. If one again aims for an MSSM-type of standard model then the analog of the condition that the 6d compact space is a Calabi-Yau manifold now is that it is a G-manifold of dimension 7.
Accordingly, models in this context go by the name G2-MSSM.
See at References - Models in M-theory.
All of the above models aim for supersymmetry in the low-energy effective field theory, because it was a wide-spread thought that this is what describes the observable world at electroweak symmetry breaking-scale. However, new experimental results at the LHC make this low energy supersymmetry scenario increasingly unlikely (even if not fully ruled out yet). Accordingly people start to look for string models now that do not display low energy supersymmetry (of course all of them have high energy local supersymmetry, in that they are theories of supergravity).
See for instance (MRS 09) and citations given there.
Technical surveys on particle physics string phenomenology include
Hans Peter Nilles, String phenomenology (2004) (pdf)
Tatsuo Kobayashi, String phenomenology (pdf)
Technical surveys on cosmological string phenomenology include
The “bottom-up approach” to string model building is attributed to
A brief review of motivations for GUT models in heterotic string theory is in
Vincent Bouchard, Ron Donagi, An SU(5) Heterotic Standard Model, Phys. Lett. B633:783-791,2006 (arXiv:hep-th/0512149)
This “heterotic standard model” has a “hidden sector” copy of the actual standard model, more details of which are discussed here:
More such “heterotic standard models” are discussed in the following articles, which aim for an “algorithmic” way of scanning the space of all semi-realistic heterotic compactifications, subject to some constraints.
A survey is here:
Original articles in this program include
The issue of moduli stabilization in these kinds of models is discussed in
Michele Cicoli, Senarath de Alwis, Alexander Westphal, Heterotic Moduli Stabilization (arXiv:1304.1809)
List of models are discussed in
Ralph Blumenhagen, Volker Braun, Boris Kors, Dieter Lüst, The Standard Model on the Quintic, Summary of Talks at SUSY02, 1st Intl. Conference on String Phenomenology in Oxford, Strings 2002 and 35th Ahrenshoop Symposium. (arXiv:hep-th/0210083)
Ching-Ming Chen, Tianjun Li, Dimitri V. Nanopoulos, Standard-Like Model Building on Type II Orientifolds, Nucl.Phys.B732:224-242,2006 (arXiv:hep-th/0509059)
Matthew J. Dolan, Sven Krippendorf, Fernando Quevedo, Towards a Systematic Construction of Realistic D-brane Models on a del Pezzo Singularity, JHEP 1110 (2011) 024 (arXiv:1106.6039)
A comprehensive account on the G2-MSSM is in
with comments on comparison to more recent experiments in
Original articles include
A survey of string model buidling without low energy susy is in
An old observation on string models without low energy susy, recently re-appreciated, is
A newer observation that received much more attention is
String Phenomenology 2002 (home page)
String Phenomenology 2003 (home page)
String Phenomenology 2004 (home page)
String Phenomenology 2005 (home page)
String Phenomenology 2006 (home page)
String Phenomenology 2007 (home page)
String Phenomenology 2008 (home page)
String Phenomenology 2009 (home page)
String Phenomenology 2010 (home page)
String Phenomenology 2013 (home page)
String Phenomenology 2014 (home page)
For a review and further pointers to the literature see at
Joseph P. Conlon, M.C. David Marsh, Searching for a 0.1-1 keV Cosmic Axion Background (arXiv:1305.3603)
Primordial decays of string theory moduli at naturally generate a dark radiation Cosmic Axion Background (CAB) with energies. This CAB can be detected through axion-photon conversion in astrophysical magnetic fields to give quasi-thermal excesses in the extreme ultraviolet and soft X-ray bands. Substantial and observable luminosities may be generated even for axion-photon couplings . We propose that axion-photon conversion may explain the observed excess emission of soft X-rays from galaxy clusters, and may also contribute to the diffuse unresolved cosmic X-ray background. We list a number of correlated predictions of the scenario.