Heterotic Z6-II MSSM Orbifolds in Blowup

TL;DR

This paper explores the connection between heterotic Z6-II orbifold models and smooth Calabi-Yau compactifications by analyzing resolutions with Abelian gauge fluxes, revealing challenges in preserving MSSM gauge groups due to anomalies.

Contribution

It provides an explicit method to solve resolution-dependent Bianchi identities and investigates the impact of blowups on MSSM-like spectra and gauge anomalies in heterotic orbifolds.

Findings

Explicit solutions to Bianchi identities are presented.

Hypercharge anomalies prevent full MSSM spectrum preservation after blowup.

Blowups at fixed points can break MSSM gauge groups due to anomalies.

Abstract

Heterotic orbifolds provide promising constructions of MSSM-like models in string theory. We investigate the connection of such orbifold models with smooth Calabi-Yau compactifications by examining resolutions of the T^6/Z6-II orbifold (which are far from unique) with Abelian gauge fluxes. These gauge backgrounds are topologically characterized by weight vectors of twisted states; one per fixed point or fixed line. The VEV's of these states generate the blowup from the orbifold perspective, and they reappear as axions on the blowup. We explain methods to solve the 24 resolution dependent Bianchi identities and present an explicit solution. Despite that a solution may contain the MSSM particle spectrum, the hypercharge turns out to be anomalous: Since all heterotic MSSM orbifolds analyzed so far have fixed points where only SM charged states appear, its gauge group can only be preserved provided that those singularities are not blown up. Going beyond the comparison of purely topological quantities (e.g. anomalous U(1) masses) may be hampered by the fact that in the orbifold limit the supergravity approximation to lowest order in alpha prime is breaking down.