Toric resolutions of heterotic orbifolds

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 2 × Z ′ 2 . We are able to obtain a direct identification between them and the known orbifold models. In the C 3 /Z 2 × Z ′ 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.

Non-abelian bundles on heterotic non-compact K3 orbifold blowups

“…With this at hand, we can consider compactifications of ten dimensional SO (32) supergravity (arising as the low energy limit of the heterotic string) on the resolved spaces in the presence of non-Abelian bundles. We provide explicit examples in the resolved C 2 /Z 3 case, and give a complete classification of all possible effective six dimensional models where the instantons are combined with Abelian gauge fluxes in order to fulfil the local Bianchi identity constraint.…”

Heterotic mini-landscape in blow-up

“…This is expected because both CY and orbifold compactifications preserve N = 1 supersymmetry. In fact, all T 6 /Z n orbifolds are singular limits of smooth CY manifolds [18][19][20][21][22][23][24][25]. In the last years there has been an intense work in understanding the transition of the heterotic string compactified on those two geometries.…”

“…The techniques of algebraic geometry in toric varieties [35][36][37] have been applied to make the orbifold singularities smooth [20,21,[23][24][25]. This process of removing the singularity and adding exceptional divisors of finite size Vol(E r ) is called blow-up or resolution, the inverse process is called blow-down.…”

Searching for the standard model in the string landscape: SUSY GUTs

“…In addition, the value of the gauge couplings at the string scale and the effective Yukawa couplings are determined by the presumed values of the vacuum expectation values [VEVs] for moduli including the dilaton, S, the bulk volume and complex structure moduli, T i , i = 1, 2, 3 and U and the SM singlet fields containing the blow-up moduli [148,167]. Finally the theory also contains a hidden sector SU(4) gauge group with QCD-like chiral matter.…”