Related papers: An Algorithmic Approach to Heterotic String Phenom…
We review the construction and classification of three-family grand unified models within the framework of asymmetric orbifolds in perturbative heterotic superstring. We give a detailed survey of all such models which is organized to aid…
Spinor--Vector Duality (SVD) has been observed in worldsheet constructions of heterotic--string compactifications. Recently, its realisation in the effective field theory limit of string vacua in six and five dimensions has been…
We construct the Neveu-Schwarz sector of heterotic string field theory using the large Hilbert space of the superghosts and the multi-string products of bosonic closed string field theory. No picture-changing operators are required as in…
We investigate different approaches to machine learning of line bundle cohomology on complex surfaces as well as on Calabi-Yau three-folds. Standard function learning based on simple fully connected networks with logistic sigmoids is…
The three string vertex for Type IIB superstrings in a maximally supersymmetric plane-wave background can be constructed in a light-cone gauge string field theory formalism. The detailed formula contains certain Neumann coefficients, which…
We further develop the numerical algorithm for computing the gauge connection of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In particular, recent work on the generalized Donaldson algorithm is extended to bundles with…
Recent work on four dimensional effective descriptions of the heterotic string has identified the moduli of such systems as being given by kernels of maps between ordinary Dolbeault cohomology groups. The maps involved are defined by the…
We give a systematic approach to constructing non-reduced, locally Cohen-Macaulay schemes with reduced support a smooth projective variety. The hierarchy of such structures includes a lot of information about the underlying variety, its…
The overarching goal of this thesis was to develop categorical methods that connect enumerative geometry, as studied in mirror symmetry, with large $N$ gauge theories. In the first part, we established a relation between graph complexes,…
Recently, string theory on Calabi--Yau manifolds was constructed and was shown to be a fully consistent, space--time supersymmetric string theory. The physically interesting case is the case of three generations. Intriguingly, it appears at…
The compactification from the 11-dimensional Horava-Witten orbifold to 5-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as is the specific $SU(4)$ vector bundle leading to the "heterotic standard model" in the…
We examine compactifications of heterotic string theory on manifolds with SU(3) structure. In particular, we study N = 1/2 domain wall solutions which correspond to the perturbative vacua of the 4D, N =1 supersymmetric theories associated…
The compactification of the heterotic string on six-dimensional orbifolds is reviewed. Some important technical aspects of their construction are clarified and new parameters, called generalized discrete torsion, are introduced and related…
We derive global consistency condition for strongly coupled heterotic string in the presence of M5-branes. Its elliptic genus is interpretable as generating functional of anomaly polynomials and so, on anomaly-free vacua, the genus is both…
We reexamine the massless spectrum of a heterotic string vacuum at large radius and present two results. The first result is to construct a vector bundle $\mathcal{Q}$ and operator $\overline{\mathcal{D}}$ whose kernel amounts to…
In these lecture notes for the Les Houches School on Applications of Random Matrices in Physics we give an introduction to the connections between matrix models and topological strings. We first review some basic results of matrix model…
We derive the five-dimensional effective action of strongly coupled heterotic string theory for the complete (1,1) sector of the theory by performing a reduction, on a Calabi-Yau three-fold, of M-theory on S^1/Z_2. A crucial ingredient for…
We construct a new class of stable vector bundles suitable for heterotic string compactifications. Using these we describe a novel way to derive the fermionic matter content of the Standard Model from the heterotic string. For this we…
We introduce the notion of the space of parallel strings with partially summable labels, which can be viewed as a geometrically constructed group completion of the space of particles with labels. We utilize this to construct a machinery…
We present a practical, algebraic method for efficiently calculating the Yukawa couplings of a large class of heterotic compactifications on Calabi-Yau three-folds with non-standard embeddings. Our methodology covers all of, though is not…