Heterotic Stringy Corrections to Metrics of Toroidal Orbifolds and Their Resolutions

Abstract

We explicitly analyse $O({\alpha }^{\prime })$ corrections to heterotic supergravity on toroidal orbifolds and their resolutions, which play important roles in string phenomenology as well as moduli stabilisation. Using a conformal factor ansatz that is valid only for four dimensional geometries, we obtain a closed expression for the $O({\alpha }^{\prime })$ metric corrections in the case of several orbifold limits of K3, namely $T^4/{\mathbb{Z}}_n$ where $n=2,3,4,6$. However, we find that non-standard embedding requires the inclusion of five-branes on such orbifolds. We also numerically investigate the behaviour around orbifold fixed points by considering the metric correction on the resolution of a ${\mathbb{C}}^2/{\mathbb{Z}}_2$ singularity. In this case, a non-trivial conformal factor can be obtained in non-standard embedding even without five-branes. In the same manner, we generalise our analysis to study metric corrections on $T^6/{\mathbb{Z}}_3$ and its resolution described by a complex line bundle over ${\mathbb{CP}}^2$. Further prospects of utilising these $O({\alpha }^{\prime })$ corrected metrics as a novel approach in obtaining realistic or semi-realistic Yukawa couplings are discussed.

Comments: 29 pages, 3 figures