Local SU(5) Unification from the Heterotic String

TL;DR

This paper constructs a 6D supergravity model derived from heterotic string compactification, featuring localized matter, partial gauge-Higgs unification, and mechanisms to address Yukawa coupling issues in grand unified theories.

Contribution

It introduces a novel 6D supergravity framework with specific orbifold compactification and anomaly cancellation, enabling realistic fermion families and Yukawa couplings.

Findings

Successful anomaly cancellation via Green-Schwarz mechanism.

Realistic fermion family structure with localized and split multiplets.

Avoidance of traditional SU(5) Yukawa coupling predictions.

Abstract

We construct a 6D supergravity theory which emerges as intermediate step in the compactification of the heterotic string to the supersymmetric standard model in four dimensions. The theory has N=2 supersymmetry and a gravitational sector with one tensor and two hypermultiplets in addition to the supergravity multiplet. Compactification to four dimensions occurs on a T^2/Z_2 orbifold which has two inequivalent pairs of fixed points with unbroken SU(5) and SU(2)xSU(4) symmetry, respectively. All gauge, gravitational and mixed anomalies are cancelled by the Green-Schwarz mechanism. The model has partial 6D gauge-Higgs unification. Two quark-lepton generations are localized at the SU(5) branes, the third family is composed of split bulk hypermultiplets. The top Yukawa coupling is given by the 6D gauge coupling, all other Yukawa couplings are generated by higher-dimensional operators at the SU(5) branes. The presence of the SU(2)xSU(4) brane breaks SU(5) and generates split gauge and Higgs multiplets with N=1 supersymmetry in four dimensions. The third generation is obtained from two split \bar{5}-plets and two split 10-plets, which together have the quantum numbers of one \bar{5}-plet and one 10-plet. This avoids unsuccessful SU(5) predictions for Yukawa couplings of ordinary 4D SU(5) grand unified theories.