nLab Gepner model



Quantum field theory

String theory



A Gepner model (Gepner 87) is a rational 2d SCFT which is a tensor product of N=2N = 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.


Boundary states

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)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

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

Lecture notes include

Further discussion in

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

See also

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

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:

Last revised on December 16, 2022 at 08:43:29. See the history of this page for a list of all contributions to it.