Explorant le paysage des compactifications de la corde hétérotique
Bernardo Fraiman · HAL (Le Centre pour la Communication Scientifique Directe) · 2022
The main goal of this thesis is to study the moduli space of a broad set of compactifications of heterotic string theory and, in particular, to find and classify the list of gauge groups that are realized in such theories. We start by analyzing the case of circle compactifications, developing a technique to compute and represent the regions of enhancement on the moduli space. Using lattice embedding techniques, we state general criteria to establish whether a gauge group is realized or not on compactifications on Tᵈ, creating a series of algorithms to completely explore these moduli spaces. For d=2, we find that the respective gauge groups coincide with all possible singular fibers of extremal K3 surfaces, corroborating the duality with F-theory on a K3 surface. We also construct a method to transform the moduli under T-duality and build the map that relates the moduli of the E₈ x E₈ and SO(32) heterotic strings on a torus. We also analyse compactifications of the heterotic string on Tᵈ/ℤ₂ asymmetric orbifolds which realize the so-called CHL string. This is of interest because the d=2 and d=3 cases are dual respectively to F-theory and M-theory on a K3 with a frozen singularity, which are not well understood. We study in detail these theories and, with some modifications to our algorithms, explore and find all the symmetry enhancements, verifying that they satisfy a condition for anomaly-free one-form center brought to light very recently. Finally, we obtain the complete list of gauge groups that are realized in the heterotic string in 7d and 6d, including the ordinary toroidal compactifications, the CHL and four other components realized via nontrivial holonomy triples. We derive a map that relates the gauge groups on the toroidal compactifications to the other components. In 7d, it coincides with the singularity freezing mechanism in M-theory on K3; while in 6d we show that the possible freezings for each gauge group are determined by its topology.