nLab string phenomenology



String theory


physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics



String phenomenology is phenomenology in particle physics and cosmology based on models that are derived or at least motivated from string theory (as effective QFTs from string vacua).

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 naturally 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 possible 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).

Top-down models and bottom-up models

Since a realistic string theoretic model is, by design, 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 N=1N=1 low energy supersymmetry in the effective 4d model).

This approach is known as the bottom-up approach to string model building (AIQU 00).

Contrary to this is the historically older top-down approach (usually attributed to (Candelas-Horowitz-Strominger-Witten 85)) in the heterotic string theory compactification models (see below).

Semi-realistic models in string theory

Examples of models in string phenomenology include

See at References - Models below.

Models in heterotic string theory

The models in heterotic string theory follow the historically original and hence oldest strategy of finding semi-realistic 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 remaining 4-dimensional space.

Since most of string model building was aimed for reproducing the minimally supersymmetric extension of the standard model of particle physics, these approaches usually take that compact 6-manifold to be a complex 3-dimensional Calabi-Yau manifold.

In more detail, the paradigm of this approach is compactification of the E8×\times E8 heterotic string theory on a Calabi-Yau manifold of Euler characteristic χ=±6\chi = \pm 6, 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 D=4D = 4, N=1N = 1 supersymmetry is assumed to take place due to some field-theoretical non-perturbative effects.

See at References - Models in heterotic string theory

The lift of these heterotic CY3-compactifications to M-theory is M-theory on G2-manifolds, discussed below.

Models in type II string theory / F-theory

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.

The intersecting branes of main relevance in type IIA string theory are D6-branes (e.g. Lüst 04, Ibanez-Uranga 12, section 10), which, under T-duality, correspond in type IIB to D7-branes. These are precisely the ones whose lift to M-theory correspond to conifold/ADE orbifold singularities of KK-monopoles, see also at F-branes – table.

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 10 50010^{500} (coming from an estimate of the number of non-trivial 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

Computer scan of Gepner-model compactifications

Discussion of string phenomenology of intersecting D-brane models KK-compactified with non-geometric fibers such that the would-be string sigma-models with these target spaces are in fact Gepner models (in the sense of Spectral Standard Model and String Compactifications) is in (Dijkstra-Huiszoon-Schellekens 04a, Dijkstra-Huiszoon-Schellekens 04b):

A plot of standard model-like coupling constants in a computer scan of Gepner model-KK-compactification of intersecting D-brane models according to Dijkstra-Huiszoon-Schellekens 04b.

The blue dot indicates the couplings in SU(5)SU(5)-GUT theory. The faint lines are NOT drawn by hand, but reflect increased density of Gepner models as seen by the computer scan.

Models in M-theory

The lift of the heterotic models compactified on Calabi-Yau manifolds to 11-dimensional supergravity with some of its “M-theory”-corrections taken into account is M-theory on G2-manifolds, hence M-theory KK-compactified on G2-manifolds (or rather: orbifolds) of, necessarily, dimension 7.

Accordingly, models in this context go by the name G2-MSSM.

See at References - Models in M-theory.

Non-supersymmetric models

All of the above models aim for N=1N = 1 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.



Useful broad survey is in

Technical surveys on particle physics string phenomenology include

Technical surveys on cosmological string phenomenology include

The “bottom-up approach” to string model building is attributed to

See also

  • Hans-Peter Nilles, Patrick K.S. Vaudrevange, Geography of Fields in Extra Dimensions: String Theory Lessons for Particle Physics, Perspectives on String Phenomenology“ (World Scientific) (arXiv:1403.1597)

For Gepner models:

  • Christian Reppel, Phenomenological Aspects of Gepner Models, 2007 (pdf)

Original articles

Heterotic string phenomenology

The historical origin of all string phenomenology is the top-down GUT-model building in heterotic string theory due to

Review and exposition:

The E 8×E 8E_8 \times E_8-heterotic string

The following articles claim the existence of exact realization of the gauge group and matter-content of the MSSM in heterotic string theory on orbifolds (not yet checking Yukawa couplings):

A computer search through the “landscape” of Calabi-Yau varieties showed severeal hundreds more such exact heterotic standard models (about one billionth of all CYs searched, and most of them arising as SU(5)-GUTs):

general computational theory:

using heterotic line bundle models:

The resulting database of heterotic line bundle models is here:

Review includes

Computation of metrics on these Calabi-Yau compactifications (eventually needed for computing their induced Yukawa couplings) is started in

This “heterotic standard model” has a “hidden sector” copy of the actual standard model, more details of which are discussed here:

The issue of moduli stabilization in these kinds of models is discussed in

Principles singling out heterotic models with three generations of fundamental particles are discussed in:

Discussion of non-supersymmetric: GUT models:

  • Alon E. Faraggi, Viktor G. Matyas, Benjamin Percival, Classification of Non-Supersymmetric Pati-Salam Heterotic String Models (arXiv:2011.04113)

See also:

  • Carlo Angelantonj, Ioannis Florakis, GUT Scale Unification in Heterotic Strings (arXiv:1812.06915)

The SemiSpin(32)SemiSpin(32)-heterotic string

Discussion of string phenomenology for the SemiSpin(32)-heterotic string (see also at type I phenomenology):

On heterotic line bundle models:

Further Models

Type II string theory models

The canonical textbook for type II superstring phenomenology via intersecting D-brane models is

The bottom-up intersecting D-brane model building originates with

See also

Reviews of intersecting D-brane model in type II string theory (in orientifold flux compactifications) include

Computer scan of Gepner model-KK-compactifications of intersecting D-brane models:

Computer scan of toroidal orbifold-KK-compactification of intersecting D-brane models:

Realistic Yukawa couplings and fermion masses in an MSSM Pati-Salam GUT model with 3 generations of fermions realized on intersecting D6-branes KK-compactified on a toroidal orbifold T 6( 2× 2)T^6\sslash (\mathbb{Z}_2 \times \mathbb{Z}_2) are claimed in

See also

  • Erik Parr, Patrick K.S. Vaudrevange, Martin Wimmer, Predicting the orbifold origin of the MSSM (arXiv:2003.01732)

Type I string theory model

Discussion for type I string theory:

  • H.S. Mani, A. Mukherjee, R. Ramachandran, A.P. Balachandran, Embedding of SU(5)SU(5) GUT in SO(32)SO(32) superstring theories, Nuclear Physics B Volume 263, Issues 3–4, 27 January 1986, Pages 621-628 (arXiv:10.1016/0550-3213(86)90277-4)

  • Luis Ibáñez, C. Muñoz, S. Rigolin, Aspects of Type I String Phenomenology, Nucl.Phys. B553 (1999) 43-80 (arXiv:hep-ph/9812397)

  • Emilian Dudas, Theory and Phenomenology of Type I strings and M-theory, Class. Quant. Grav.17:R41-R116, 2000 (arXiv:hep-ph/0006190)

  • Naoki Yamatsu, String-Inspired Special Grand Unification (arXiv:1708.02078)

F-Theory models

Discussion of GUT models via F-theory is in

A direct geometric engineering of the MSSM within F-theory is claimed in

  • Mirjam Cvetič, Ling Lin, Muyang Liu, Paul-Konstantin Oehlmann, An F-theory Realization of the Chiral MSSM with 2\mathbb{Z}_2-Parity (arXiv:1807.01320)

Discussion of the exact gauge group of the standard model of particle physics, G=(SU(3)×SU(2)×U(1))/ 6G = \big( SU(3) \times SU(2) \times U(1)\big)/\mathbb{Z}_6 including its 6\mathbb{Z}_6-quotient (see there) and the exact fermion field content, realized in F-theory is in

  • Denis Klevers, Damian Kaloni Mayorga Pena, Paul-Konstantin Oehlmann, Hernan Piragua, Jonas Reuter, F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches, JHEP01(2015)142 (arXiv:1408.4808)

  • Mirjam Cvetic, Ling Lin, section 3.3 of The global gauge group structure of F-theory compactifications with U(1)U(1)s (arXiv:1706.08521)

Based on this, a large number of realizations of the exact field content of the standard model of particle physics (or rather the MSSM) in F-theory is claimed to be realized in

M-theory models

A comprehensive account on models in M-theory on G2-manifolds and the G2-MSSM is in

with comments on comparison to more recent experiments in

  • Gordon Kane, Ran Lu, Bob Zheng, Review and Update of the Compactified M/string Theory Prediction of the Higgs Boson Mass and Properties, Int. J. Mod. Phys. A Volume 28 (2013) 1330002 (arXiv:1211.2231)

Original articles include

See also

Alternatively, discussion in Hořava-Witten theory:

Heterotic M-theory models

Discussion in heterotic M-theory:

and with emphasis on heterotic line bundle-models:

Non-supersymmetric models

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 conferences

String cosmic inflation

In string theory the inflaton field for models of cosmic inflation field can be modeled by various effects, such as

For a review and further pointers to the literature see at

  • Cliff Burgess, M. Cicoli, F. Quevedo, String Inflation After Planck 2013 (arXiv:1306.3512)

Axion phenomenology

On stringy axion phenomenology:

  • 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 z10 12z \sim 10^{12} naturally generate a dark radiation Cosmic Axion Background (CAB) with 0.11keV0.1 - 1 keV 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 10 11GeV 1\ll 10^{-11} GeV^{-1}. 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.

Last revised on March 22, 2023 at 12:41:16. See the history of this page for a list of all contributions to it.