Strings on freely acting orbifolds: Spectra, moduli spaces and branes

Abstract

In this dissertation, we study various aspects of type IIB string theory compactified on freely acting orbifolds. We focus particularly on asymmetric orbifolds, which are examples of non-geometric string compactifications and constitute an intriguing corner in the string landscape. We describe the orbifolds using two complementary approaches; the duality twists and the lattice approach. First, we discuss the general construction of freely acting (asymmetric) orbifolds, focusing on the closed string sector. Afterwards, we present explicit examples of orbifolds preserving $\mathcal{N} = 6,4,2$ or $0$ supersymmetry in five dimensions and we demonstrate the connection between freely acting orbifolds and Scherk-Schwarz reductions by matching the lightest untwisted orbifold states with those arising form the effective supergravity theory. Regarding the orbifold twisted sectors, we show that at special points in the moduli space, generically massive states can become massless. Furthermore, we show that the spectrum of non-supersymmetric orbifolds can become tachyon-free away from special loci in the moduli space. Next, we turn our attention to the orbifold moduli space, and we focus on orbifolds preserving $\mathcal{N} = 2$ supersymmetry in five dimensions, for which we determine the classical hypermultiplet and vector multiplet moduli spaces. Moreover, by constructing dual orbifold pairs, we argue that no quantum corrections to the metric on the vector multiplet moduli space arise. Then, we discuss aspects of the swampland program in the context of freely acting asymmetric orbifolds and we verify that the swampland distance conjecture is valid in the non-geometric compactifications of string theory studied in this thesis. Finally, we focus on the D-brane spectrum of freely acting orbifolds and we determine the conditions under which the various D-branes survive the orbifolding.

Figures (8)

• Figure 1: An open string with two end-points (left), and a closed string forming a loop (right).
• Figure 2: An open string world-sheet (left), and a closed string world-sheet (right). Time evolves upwards.
• Figure 3: A two-dimensional cylinder of tiny radius appears to be a one-dimensional line. The picture is taken fromhetLam:2020goj.
• Figure 4: The orbifold $S^1/\mathbb{Z}_2$ (right figure). Here, the $\mathbb{Z}_2$ action is the reflection $z\to -z$. The picture is taken frombassant.
• Figure 5: The orbifold $S^1/\mathbb{Z}_2'$ (right figure). Here, the $\mathbb{Z}_2'$ action is the translation $z\to z+\pi R$. The picture is taken frombassant.