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Contents

Idea

A Gepner model (Gepner 87) is a rational 2d SCFT which is a tensor product of $N = 2$ super-minimal model CFT.

This means that Gepner models are “non-geometric string vacua” in that they do not arise as sigma-models with target space a smooth manifold. Indeed the Gepner models appear as the limiting cases of sigma-models with target space a 6d Calabi-Yau manifold at singular points in the moduli space of the CY target: the flop transition.

As such the Gepner models are directly analogous to the purely algebraically defined non-classical fibers in the Connes-Lott-Chamseddine-Barrett model (it is a “2-spectral triple”-analog of the spectral triples in the Connes-Lott model, see there) and, accordingly, plays a central role in string phenomenology (for review see e.g. Reppel 07).

The Gepner models are a basic building block for rational conformal field theory.

Properties

Boundary states

All the known rational boundary states for Gepner models can be regarded as permutation branes.

(Enger-Recknagel-Roggenkamp 05)

Phenomenology

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

Related concepts

• WZW model

• Kazama-Suzuki model

• heterotic string, type II superstring

• KK-compactification

References

The original article is

• Doron Gepner, Space-time supersymmetry in compactified string theory and superconformal models , Nucl. Phys. B296 B (1987) 757.296 (1987) 757 []

Lecture notes include include:

• Doron Gepner, Lectures On $N=2$ String Theory , 1989 ( [pdf , spire:277718/]spire:277718/)

Further discussion in

• Maximilian Kreuzer, Heterotic $(0,2)$ Gepner Models and Related Geometries, in Fundamental Interactions, pp. 335-362 World Scientific (2009) (arXiv:0904.4467, doi:10.1142/9789814277839_0019)

See also the references at flop transition for more.

Review of application in string phenomenology includes

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

D-branes in string theory vacua defined by Gepner model SCFTs are discussed, via boundary conformal field theory in

• Jürgen Fuchs, Christoph Schweigert, J. Walcher, Projections in string theory and boundary states for Gepner models, Nucl.Phys. B588 (2000) 110-148 (arXiv:hep-th/0003298)

  (with emphasis on GSO projections)

• Jürgen Fuchs, P. Kaste, Wolfgang Lerche, C. Lutken, Christoph Schweigert, J. Walcher, Boundary Fixed Points, Enhanced Gauge Symmetry and Singular Bundles on K3, Nucl.Phys.B598:57-72, 2001 (arXiv:hep-th/0007145)

See also

• Andreas Recknagel, Volker Schomerus, D-branes in Gepner models, Nucl.Phys. B531 (1998) 185-225 (arXiv:hep-th/9712186)

• Volker Braun, Sakura Schafer-Nameki, D-Brane Charges in Gepner Models, J. Math. Phys. 47 (2006) 092304 (arXiv:hep-th/0511100)

Discussion of permutation D-branes for Gepner models, via boundary conformal field theory, includes

• Håkon Enger, Andreas Recknagel, Daniel Roggenkamp, Permutation branes and linear matrix factorisations, JHEP0601:087, 2006 (arXiv:hep-th/0508053)

Gepner model orientifolds:

• Brandon Bates, Charles Doran, Koenraad Schalm, Crosscaps in Gepner Models and the Moduli space of T2 Orientifolds, Advances in Theoretical and Mathematical Physics, Volume 11, Number 5, 839-912, 2007 (arXiv:hep-th/0612228)

Specifically string phenomenology and the landscape of string theory vacua of Gepner model orientifold compactifications:

• T.P.T. Dijkstra, L. R. Huiszoon, Bert Schellekens, Chiral Supersymmetric Standard Model Spectra from Orientifolds of Gepner Models, Phys.Lett. B609 (2005) 408-417 (arXiv:hep-th/0403196)

• T.P.T. Dijkstra, L. R. Huiszoon, Bert Schellekens, Supersymmetric Standard Model Spectra from RCFT orientifolds, Nucl.Phys.B710:3-57,2005 (arXiv:hep-th/0411129)

• Fernando Marchesano, Bert Schellekens, Timo Weigand, Sec. 4 of: D-brane and F-theory Model Building [[arXiv:2212.07443](https://arxiv.org/abs/2212.07443)]