Related papers: TASI Lectures on Geometric Tools for String Compac…
We investigate special compactifications of the heterotic string for which the space of half-BPS states is, in a natural way, a representation of various subgroups of the Conway group. These compactifications provide a useful framework for…
Calabi-Yau (CY) manifolds play a ubiquitous role in string theory. As a supersymmetry-preserving choice for the 6 extra compact dimensions of superstring compactifications, these spaces provide an arena in which to explore the rich…
In these lecture proceedings, we describe some of the fundamental mathematical concepts that underlie supersymmetric string theory and field theory, and their role in describing and testing dualities. In particular, we provide a pedagogical…
We review a progress in obtaining the complete non-perturbative effective action of type II string theory compactified on a Calabi-Yau manifold. This problem is equivalent to understanding quantum corrections to the metric on the…
The goal of identifying the Standard Model of particle physics and its extensions within string theory has been one of the principal driving forces in string phenomenology. Recently, the incorporation of artificial intelligence in string…
These lectures provide a self-contained introduction to flux compactifications of type IIB string theory on Calabi-Yau orientifolds. The first lecture begins with geometric foundations, then presents vacuum solutions in Calabi-Yau…
The structure of stringy quantum corrections to four-dimensional effective theories is particularly interesting for string phenomenology and attempts to stabilize moduli. We consider the heterotic string compactified on a Calabi-Yau space.…
We use local mirror symmetry in type IIA string compactifications on Calabi-Yau n+1 folds $X_{n+1}$ to construct vector bundles on (possibly singular) elliptically fibered Calabi-Yau n-folds Z_n. The interpretation of these data as valid…
We approach string phenomenology from the perspective of computational algebraic geometry, by providing new and efficient techniques for proving stability and calculating particle spectra in heterotic compactifications. This is done in the…
We describe a new class of supersymmetric string compactifications to 4d Minkowski space. These solutions involve type II strings propagating on (orientifolds of) non Calabi-Yau spaces in the presence of background NS and RR fluxes. The…
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…
Supersymmetric heterotic string models, built from a stable holomorphic vector bundle $V$ on a Calabi-Yau threefold $X$, usually come with many vector bundle moduli whose stabilisation is a difficult and complex task. It is therefore of…
In this paper we study string compactifications on Deligne-Mumford stacks. The basic idea is that all such stacks have presentations to which one can associate gauged sigma models, where the group gauged need be neither finite nor…
Superstring theories are the most promising theories for unified description of all fundamental interactions including gravity. However, these theories are formulated consistently only in 10 spacetime dimensions. Therefore, to connect to…
This is a review. Comments are welcome. The observation that the structure of string theory is rich enough to include the standard model in rough outline is an old one, starting with the early constructions of free field constructions,…
In this thesis we have studied various applications of asymptotic Hodge theory in string compactifications. This mathematical framework captures how physical couplings of the resulting effective theories behave near field space boundaries…
We construct spacetime supersymmetric, modular invariant partition functions of strings on the conifold-type singularities which include contributions from the discrete-series representations of SL(2, R). The discrete spectrum is…
In order to be in control of the $\alpha'$ derivative expansion, geometric string compactifications are understood in the context of a large volume approximation. In this letter, we consider the reduction of these higher derivative terms,…
We study supersymmetric compactification to four dimensions with non-zero H-flux in heterotic string theory. The background metric is generically conformally balanced and can be conformally Kahler if the primitive part of the H-flux…
We review recent progress in understanding non-perturbative instanton corrections to the hypermultiplet moduli space in type II string compactifications on Calabi-Yau threefolds.