Abstract
Compactifications of the heterotic string on special Td/ℤ2 orbifolds realize a landscape of string models with 16 supercharges and a gauge group on the left-moving sector of reduced rank d + 8. The momenta of untwisted and twisted states span a lattice known as the Mikhailov lattice II(d), which is not self-dual for d > 1. By using computer algorithms which exploit the properties of lattice embeddings, we perform a systematic exploration of the moduli space for d ≤ 2, and give a list of maximally enhanced points where the U(1)d+8 enhances to a rank d + 8 non-Abelian gauge group. For d = 1, these groups are simply-laced and simply-connected, and in fact can be obtained from the Dynkin diagram of E10. For d = 2 there are also symplectic and doubly-connected groups. For the latter we find the precise form of their fundamental groups from embeddings of lattices into the dual of II(2). Our results easily generalize to d > 2.
Highlights
The rich landscape of string theory can be charted with a high level of rigor in regions where there is a full world-sheet description
By using computer algorithms which exploit the properties of lattice embeddings, we perform a systematic exploration of the moduli space for d ≤ 2, and give a list of maximally enhanced points where the U(1)d+8 enhances to a rank d + 8 non-Abelian gauge group
In a previous work [4] we developed an algorithm for T d compactifications which, starting from a point p0 of the moduli space corresponding to a gauge group of maximal rank rmax = d + 16, gives a set of new points of maximal enhancement
Summary
The rich landscape of string theory can be charted with a high level of rigor in regions where there is a full world-sheet description. With the motivation to get a better understanding of the landscape of string theory, in this paper we extend the analysis of [4] to compactifications of the E8 × E8 heterotic string on T d/Z2 asymmetric orbifolds which realize the so-called CHL string [9, 10] (in 10 − d dimensions with d ≥ 1) This Z2 acts by exchanging the two E8 components of the momentum lattice, together with a shift by half a period along one of the compact directions. For d = 2, the algorithm generates a list of 61 groups of maximal enhancement In this case, the CHL string is a realisation of the anomaly free theories with 16 supercharges and rank 10 gauge groups [12]. The world-sheet realisation of the space-time gauge symmetries is briefly discussed in appendix B
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