Elliptic Calabi-Yau Threefolds with Z_3 x Z_3 Wilson Lines

TL;DR

This paper constructs a specific class of elliptic Calabi-Yau threefolds with Z_3 x Z_3 symmetry, exploring their geometric properties and implications for particle physics models with realistic features.

Contribution

It introduces a new construction of elliptic Calabi-Yau threefolds with Z_3 x Z_3 fundamental group and analyzes their potential for realistic particle physics model building.

Findings

Realistic three-generation models with right-handed neutrinos

Suppression of nucleon decay via U(1)_{B-L} gauge factor

Detailed analysis of moduli space and cohomology

Abstract

A torus fibered Calabi-Yau threefold with first homotopy group Z_3 x Z_3 is constructed as a free quotient of a fiber product of two dP_9 surfaces. Calabi-Yau threefolds of this type admit Z_3 x Z_3 Wilson lines. In conjunction with SU(4) holomorphic vector bundles, such vacua lead to anomaly free, three generation models of particle physics with a right handed neutrino and a U(1)_{B-L} gauge factor, in addition to the SU(3)_C x SU(2)_L x U(1)_Y standard model gauge group. This factor helps to naturally suppress nucleon decay. The moduli space and Dolbeault cohomology of the threefold is also discussed.