A Solution to the Doublet-Triplet Splitting Problem in the Type IIB Supergravity

TL;DR

This paper constructs a supersymmetric brane world model in Type IIB supergravity that addresses the doublet-triplet splitting problem in GUTs, using orbifold compactification and D-brane fluctuations.

Contribution

It provides an explicit realization of product-group unification models within Type IIB supergravity, connecting them to brane world scenarios and orbifold compactifications.

Findings

Successful realization of GUT symmetry breaking sector from D-brane fluctuations

Introduction of three quark and lepton families at orbifold singularities

Discussion of anomaly cancellation and R symmetry in the model

Abstract

The doublet--triplet mass splitting problem is one of the most serious problems in supersymmetric grand unified theories (GUTs). A class of models based on a product gauge group, such as the SU(5)_{GUT} times U(3)_H or the SU(5)_{GUT} times U(2)_H, realize naturally the desired mass splitting that is protected by an unbroken R symmetry. It has been pointed out that various features in the models suggest that these product-group unification models are embedded in a supersymmetric brane world. We show an explicit construction of those models in the supersymmetric brane world based on the Type IIB supergravity in ten dimensions. We consider T^6/(Z_{12} times Z_2) orientifold for the compactified six extra dimensions. We find that all of the particles needed for the GUT-symmetry-breaking sector are obtained from the D-brane fluctuations. The three families of quarks and leptons are introduced at an orbifold singularity, although their origin remains unexplained. This paper includes extensive discussion on anomaly cancellation in a given orbifold geometry. Relation to the Type IIB string theory, realization of R symmetry as a rotation of extra-dimensional space, and effective superpotential at low energies are also discussed.