Towards Mirror Symmetry with Semi-Realistic Intersecting Brane Configurations

TL;DR

This paper explores a T6 orbifold compactification using a Landau-Ginzburg model perspective, employing matrix factorizations and mirror symmetry to analyze intersecting brane configurations and their potential for realistic string models.

Contribution

It introduces a novel approach to studying intersecting branes via Landau-Ginzburg models and matrix factorizations, providing a new perspective on mirror symmetry applications in string compactifications.

Findings

Demonstrates the use of matrix factorizations for D-branes in orbifold models

Maps features from B-model to A-model via mirror symmetry

Establishes a basis for extending mirror symmetry analysis to realistic models

Abstract

A T6 orbifold compactification is discussed from the somewhat unconventional perspective as the large radius limit of a Landau-Ginzburg model. The features of the model are in principle familiar, but the way they enter here is different from the way they enter when using more commonly used methods. It is hoped that the point of view presented here can supplement the understanding of the features used in string compactifications, notably in terms of naturalness and completeness. More precisely, the analyzed T6 / Z_4 x Z_4 features two different kinds of O-planes, branes in the bulk as well as fractional branes, continuous and discrete Wilson lines as well as an orientifold action which can act in different ways on the Wilson lines. The D-branes are desribed by matrix factorizations. This work is also intended to be a showcase for the potentials of matrix factorizations which are for the first time geared to their full level of sophistication in this paper. Throughout the analyis everything is mapped from the B-model side of the LG-model to the A side by mirror symmetry. The work could be extended straightforwardly yet tediously to perform mirror symmetry on a general intersecting brane configuration and to compute Yukawa couplings. The analysis presented here can also be applied to non-toroidal backgrounds with an intersecting brane configuration on it, so I hope that it will be a helpful basis for later applications of mirror symmetry to models exhibiting real world properties.