Taming Triangulation Dependence of T6/Z2xZ2 Resolutions

TL;DR

This paper introduces a parameterization method to handle triangulation dependence in T6/Z2xZ2 orbifold resolutions, enabling consistent calculations of topological invariants and line bundle models across different triangulations.

Contribution

The authors develop a novel parameterization approach that tracks all triangulations simultaneously, simplifying the analysis of resolutions and their associated physical models.

Findings

Parameterization allows calculation of intersection numbers and Chern classes for any triangulation.

Stronger consistency conditions for line bundle models are derived from superimposing Bianchi identities.

Admissibility of flop-transitions between triangulations is established under certain conditions.

Abstract

Resolutions of certain toroidal orbifolds, like T6/Z2xZ2, are far from unique, due to triangulation dependence of their resolved local singularities. This leads to an explosion of the number of topologically distinct smooth geometries associated to a single orbifold. By introducing a parameterisation to keep track of the triangulations used at all resolved singularities simultaneously, (self-)intersection numbers and integrated Chern classes can be determined for any triangulation configuration. Using this method the consistency conditions of line bundle models and the resulting chiral spectra can be worked out for any choice of triangulation. Moreover, by superimposing the Bianchi identities for all triangulation options much simpler though stronger conditions are uncovered. When these are satisfied, flop--transitions between all different triangulations are admissible. Various methods are exemplified by a number of concrete models on resolutions of the T6/Z2xZ2 orbifold.