Orbifold resolutions with general profile

TL;DR

This paper explores a broad class of orbifold resolutions and demonstrates that localized chiral fermions emerge at fixed points, with their properties independent of the resolution details, confirmed through numerical analysis.

Contribution

It introduces a general resolution framework for orbifolds and shows the resulting chiral fermion spectrum matches previous specific cases, confirming the robustness of the resolution method.

Findings

Localized chiral fermions appear at fixed points regardless of resolution details.

The mass spectrum and wave functions converge to orbifold results in the limit.

Numerical studies validate the resolution approach for S^1/Z_2.

Abstract

A very general class of resolved versions of the C/Z_N, T^2/Z_N and S^1/Z_2 orbifolds is considered and the free theory of 6D chiral fermions studied on it. As the orbifold limit is taken, localized 4D chiral massless fermions are seen to arise at the fixed points. Their number, location and chirality is found to be independent on the detailed profile of the resolving space and to agree with the result of hep-th/0409229, in which a particular resolution was employed. As a consistency check of the resolution procedure, the massive equation is numerically studied. In particular, for S^1/Z_2, the "resolved" mass--spectrum and wave functions in the internal space are seen to correctly reproduce the usual orbifold ones, as the orbifold limit is taken.