Torus-Fibered Calabi-Yau Threefolds with Non-Trivial Fundamental Group

TL;DR

This paper constructs new Calabi-Yau threefolds with non-trivial fundamental groups by fiber product methods, enabling the development of particle physics models with suppressed nucleon decay.

Contribution

It introduces a novel construction of Calabi-Yau threefolds with fundamental group Z_2 x Z_2 using fiber products of rational elliptic surfaces with specific automorphisms.

Findings

Constructed smooth Calabi-Yau threefolds with fundamental group Z_2 x Z_2

Demonstrated the existence of stable, holomorphic SU(4) vector bundles on these spaces

Enabled particle physics models with suppressed nucleon decay

Abstract

We construct smooth Calabi-Yau threefolds Z, torus-fibered over a dP_9 base, with fundamental group Z_2 X Z_2. To do this, the structure of rational elliptic surfaces is studied and it is shown that a restricted subset of such surfaces admit at least a Z_2 X Z_2 group of automorphisms. One then constructs Calabi-Yau threefolds X as the fiber product of two such dP_9 surfaces, demonstrating that the involutions on the surfaces lift to a freely acting Z_2 X Z_2 group of automorphisms on X. The threefolds Z are then obtained as the quotient Z=X/(Z_2 X Z_2). These Calabi-Yau spaces Z admit stable, holomorphic SU(4) vector bundles which, in conjunction with Z_2 X Z_2 Wilson lines, lead to standard-like models of particle physics with naturally suppressed nucleon decay.