Related papers: Deconstruction, G_2 Holonomy, and Doublet-Triplet …
The mathematical features of a string theory compactification determine the physics of the effective four-dimensional theory. For this reason, understanding the mathematical structure of the possible compactification spaces is of profound…
Compactifications of M-theory on manifolds with reduced holonomy arise as the local eleven-dimensional description of D6-branes wrapped on supersymmetric cycles in manifolds of lower dimension with a different holonomy group. Whenever the…
A solution of the doublet-triplet splitting problem in the supersymmetric $SU(6)$ gauge theory is suggested. The `missing doublet' multiplet -- 175-plet of the $SU(6)$ group as well as the custodial $SU(2)_{cus}$ global symmetry play…
It is shown that natural doublet-triplet splitting can be achieved in a relatively simple way in supersymmetric SU(N)X U(1) models with N>5.
We summarize some recent progress in constructing four-dimensional supersymmetric chiral models from Type II orientifolds. We present the construction a supersymmetric Standard-like Model and a supersymmetric GUT model to illustrate the new…
We consider Grand Unified Theories based on $SO(10)$ which originate from $M$ theory on $G_2$ manifolds. In this framework we are naturally led to a novel solution of the doublet-triplet splitting problem involving an extra $\overline{{\bf…
Using an algebraic orbifold method, we present non-commutative aspects of $G_2$ structure of seven dimensional real manifolds. We first develop and solve the non commutativity parameter constraint equations defining $G_2$ manifold algebras.…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
It is shown, using a modification of an idea of Sen, that completely realistic supersymmetric grand-unified theories based on SU(6) or larger unitary groups can be constructed using the sliding-singlet mechanism. These models have a simple…
In this paper, we provide different splitting methods for solving distributionally robust optimization problems in cases where the uncertainties are described by discrete distributions. The first method involves computing the proximity…
We study a gauge coupling unification scenario based on a non-supersymmetric 5-dimensional model. Through an orbifold compactification, we obtain the Standard Model with split multiplets on a 4-dimensional wall, which is compatible with a…
M theory compactifications on G_2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We…
Algorithms that decompose a manifold into simple pieces reveal the geometric and topological structure of the manifold, showing how complicated structures are constructed from simple building blocks. This note describes a way to…
A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…
We construct global F-theory GUT models on del Pezzo surfaces in compact Calabi-Yau fourfolds realized as complete intersections of two hypersurface constraints. The intersections of the GUT brane and the flavour branes as well as the gauge…
Arnold, Falk, & Winther, in "Finite element exterior calculus, homological techniques, and applications" (2006), show how to geometrically decompose the full and trimmed polynomial spaces on simplicial elements into direct sums of…
Here we study the deformations of associative submanifolds inside a G_2 manifold M^7 with a calibration 3-form \phi. A choice of 2-plane field \Lambda on M (which always exits) splits the tangent bundle of M as a direct sum of a…
We investigate gauge coupling unification in higher dimensional GUT models with split supersymmetry. We focus on 5d and 6d orbifold GUTs, which permit a simple solution to several problems of 4D GUTs as well as control over GUT scale…
The structure-preserving doubling algorithm (SDA) is a fairly efficient method for solving problems closely related to Hamiltonian (or Hamiltonian-like) matrices, such as computing the required solutions to algebraic Riccati equations.…
We study two-stage stochastic optimization models with mixed-integer decision variables appearing in both stages. For these models, dual decomposition enables parallel computing implementation and can quickly provide a lower bound for the…