Contents

# 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.

### 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.

## References

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

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

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 1, 2019 at 13:24:41. See the history of this page for a list of all contributions to it.