Resolutions of C^n/Z_n Orbifolds, their U(1) Bundles, and Applications to String Model Building

TL;DR

This paper constructs and analyzes resolutions of C^n/Z_n orbifolds with gauge bundles, exploring their implications for string model building and demonstrating how blowup models relate to orbifold models and S-duality.

Contribution

It introduces explicit blowup constructions of C^n/Z_n orbifolds with various gauge bundles, linking these to heterotic models and revealing multiple blowdown models.

Findings

Finite U(1) bundle models due to Bianchi identity

Orbifold gauge shifts can be derived from gauge backgrounds

Multiple blowdown models exist for certain orbifolds

Abstract

We describe blowups of C^n/Z_n orbifolds as complex line bundles over CP^{n-1}. We construct some gauge bundles on these resolutions. Apart from the standard embedding, we describe U(1) bundles and an SU(n-1) bundle. Both blowups and their gauge bundles are given explicitly. We investigate ten dimensional SO(32) super Yang-Mills theory coupled to supergravity on these backgrounds. The integrated Bianchi identity implies that there are only a finite number of U(1) bundle models. We describe how the orbifold gauge shift vector can be read off from the gauge background. In this way we can assert that in the blow down limit these models correspond to heterotic C^2/Z_2 and C^3/Z_3 orbifold models. (Only the Z_3 model with unbroken gauge group SO(32) cannot be reconstructed in blowup without torsion.) This is confirmed by computing the charged chiral spectra on the resolutions. The construction of these blowup models implies that the mismatch between type-I and heterotic models on T^6/Z_3 does not signal a complication of S-duality, but rather a problem of type-I model building itself: The standard type-I orbifold model building only allows for a single model on this orbifold, while the blowup models give five different models in blow down.