A Gepner model (Gepner 87) is a rational CFT 2d SCFT which is a tensor product of $N = 2$ super-minimal model CFT.
This means that Gepner models are “non-geometric” 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.
All the known rational boundary states for Gepner models can be regarded as permutation branes.
(Enger-Recknagel-Roggenkamp 05)
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.
The original article is
Lecture notes include
See also the references at flop transition for more.
Review of application in string phenomenology includes
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
Discussion of string phenomenology and the landscape of string theory vacua of Gepner model compactifications is in
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)
Last revised on October 29, 2018 at 10:30:27. See the history of this page for a list of all contributions to it.