Related papers: Mathieu Moonshine and N=2 String Compactifications
We show that non-trivial SU(3) structures can be constructed on large classes of Calabi-Yau three-folds. Specifically, we focus on Calabi-Yau three-folds constructed as complete intersections in products of projective spaces, although we…
The study of the geometry of Calabi-Yau fourfolds is relevant for compactifications of string theory, M-theory, and F-theory to various dimensions. In the first part of this thesis, we study the action of mirror symmetry on two-dimensional…
We consider the 33 conjugacy classes of genus zero, torsion-free modular subgroups, computing ramification data and Grothendieck's dessins d'enfants. In the particular case of the index 36 subgroups, the corresponding Calabi-Yau threefolds…
The period geometry of Calabi-Yau $n$-folds, characterised by their variations of Hodge structure governed by Griffiths transversality, a graded Frobenius algebra, an integral monodromy and an intriguing arithmetic structure, is analysed…
We study the duality between M-theory compactified on Calabi-Yau fourfolds and the heterotic string compactified on Calabi-Yau threefolds times a circle. Our analysis is based on a comparison of the low energy effective actions in three…
In this note we compare the moduli spaces of the heterotic string compactified on a two-torus and F-Theory compactified on an elliptic K3 surface for the case of an unbroken E8 x E8 gauge group. The explicit map relating the deformation…
In snapshots, this exposition introduces conformal field theory, with a focus on those perspectives that are relevant for interpreting superconformal field theory by Calabi-Yau geometry. It includes a detailed discussion of the elliptic…
In this paper we describe the heterotic dual of the type IIB theory compactified to four dimensions on a toroidal orientifold in the presence of fluxes. The type IIB background is most easily described in terms of an M-theory…
We extend the investigation of special toroidal compactifications of heterotic string theory for which the half-BPS states provide representations of subgroups of the Conway group. We also explore dual descriptions of these theories and…
For a given complex n-fold M we present an explicit construction of all complex (n+1)-folds which are principal holomorphic T2-fibrations over M. For physical applications we consider the case of M being a Calabi-Yau 2-fold. We show that…
In this thesis we study compactifications of type II string theories and M-theory to four dimensions. We construct the four-dimensional N=2 supergravities that arise from compactifications of type IIA string theory and M-theory on manifolds…
We identify the auxiliary fields in the hypermultiplets of type IIB string theory compactified on a Calabi-Yau manifold, using a combination of worldsheet and supergravity techniques. The SUSY-breaking squark and gaugino masses in type IIB…
We revisit the proposal of arXiv:2104.05716 for the worldsheet description of string theory compactifications on special holonomy manifolds obtained via connected sums: the geometric construction corresponds to a diamond of inclusions of…
We review several aspects of heterotic, type II, F-theory, and M-theory compactifications on Calabi-Yau threefolds and fourfolds. In the context of dualities we focus on the heterotic gauge structure determined by the various types of…
The analogue of the McKay-Thompson series for the proposed Mathieu group action on the elliptic genus of K3 is analysed. The corresponding NS-sector twining characters have good modular properties and satisfy remarkable replication…
We discuss how transitions in the space of heterotic K3*T^2 compactifications are mapped by duality into transitions in the space of Type II compactifications on Calabi-Yau manifolds. We observe that perturbative symmetry restoration, as…
In this thesis, we explore two approaches to string phenomenology. In the first half of the work, we investigate M-theory compactifications on spaces with co-dimension four, orbifold singularities. We construct M-theory on C^2/Z_N by…
We study quantum effects in five dimensions in heterotic superstring theory compactified on K_3 x S_1 and analyze the conjecture that its dual effective theory is eleven-dimensional supergravity compactified on a Calabi-Yau threefold. This…
The condition of having an $N=1$ spacetime supersymmetry for heterotic string leads to 4 distinct possibilities for compactifications namely compactifications down to 6,4,3 and 2 dimensions. Compactifications to 6 and 4 dimensions have been…
Even a cursory inspection of the Hodge plot associated with Calabi-Yau threefolds that are hypersurfaces in toric varieties reveals striking structures. These patterns correspond to webs of elliptic-K3 fibrations whose mirror images are…