Heterotic ℤ_6–IIMSSM orbifolds in blowup

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 / 6-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 α ′ is breaking down.

A zip-code for quarks, leptons and Higgs bosons

“…Here we concentrate on translational embeddings only. Consider the map Table 1: Fixed points of the T 1 and T 5 sectors [34]. Each combination abc leads to an inequivalent singularity on the orbifold.…”

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.…”

(MS)SM‐like models on smooth Calabi‐Yau manifolds from all three heterotic string theories

“…Even though all three of them were roughly discovered around the same time, essentially only the E 8 ×E 8 theory has been examined in string model building on Calabi-Yau manifolds in a more systematic fashion. On smooth compact orbifold resolutions semirealistic models were obtained from the E 8 ×E 8 theory using line bundles [1][2][3]. In the class of favorable Complete Intersection Calabi-Yaus (CICYs) with discrete symmetries, specific S(U(1) 5 ) line bundle constructions embedded in a single E 8 factor have been investigated in [4][5][6].…”