Toric Resolutions of Heterotic Orbifolds

TL;DR

This paper explores heterotic orbifold resolutions using toric geometry, providing new methods to construct and identify consistent blowup models, and illustrating these with explicit examples.

Contribution

It introduces a toric geometric approach to heterotic orbifold resolutions and demonstrates its application through explicit models and comparisons with known orbifold constructions.

Findings

Integral computations match toric divisor integrals.

Explicit heterotic models constructed on resolved orbifolds.

Only one resolution allows fully consistent heterotic blowup models.

Abstract

We investigate resolutions of heterotic orbifolds using toric geometry. Our starting point is provided by the recently constructed heterotic models on explicit blowup of C^n/Z_n singularities. We show that the values of the relevant integrals, computed there, can be obtained as integrals of divisors (complex codimension one hypersurfaces) interpreted as (1,1)-forms in toric geometry. Motivated by this we give a self contained introduction to toric geometry for non-experts, focusing on those issues relevant for the construction of heterotic models on toric orbifold resolutions. We illustrate the methods by building heterotic models on the resolutions of C^2/Z_3, C^3/Z_4 and C^3/Z_2xZ_2'. We are able to obtain a direct identification between them and the known orbifold models. In the C^3/Z_2xZ_2' case we observe that, in spite of the existence of two inequivalent resolutions, fully consistent blowup models of heterotic orbifolds can only be constructed on one of them.