Matter from Toric Geometry and its Search at the LHC

T.V Obikhod

doi:10.13189/ujpa.2013.010207

Abstract

Toric geometry is applied for construction the enhanced gauge groups in F-theory compactified on elliptic Calabi-Yau fourfolds. The Hodge numbers calculated from the polyhedra for the chain H = SU (1), ... ,SU (5), SO(10), E6, E7 determine the number of tensor multiplets, vector multiplets and hypermultiplets of soli- tonic states that appear from singularities of elliptic fibration. Due to duality between the compactification of E8timesE8 heterotic string and the type IIA string compactification on a Calabi-Yau manifold there is a natural sequence of E-group embeddings which gives the matter content of Minimal Supersymmetric Standard Model and the possibility of searching for supersymmetry at the LHC.

Highlights

At high energy, the three gauge interactions which define the electromagnetic, weak, and strong interactions, are merged into one single interaction characterized by one larger gauge symmetry Grand Unified Theory, (GUT) [1] and one unified coupling constant
There is a natural sequence of group embeddings which gives the Minimal Supersymmetric Standard Model gauge group and matter structure that can be detected at the LHC [5]
We see the duality between the compactifications of the E8 × E8 heterotic string and the type IIA string compactification on a Calabi-Yau manifold

Summary

Introduction

The three gauge interactions which define the electromagnetic, weak, and strong interactions, are merged into one single interaction characterized by one larger gauge symmetry Grand Unified Theory, (GUT) [1] and one unified coupling constant This gauge coupling unification works quite well in the Minimal Supersymmetric Standard Model (MSSM) motivating grand unification (or some superstring theories with similar properties) and that supersymmetry emerges. Supersymmetry refers to possible relations between the spectrum and interactions of fermions (half-integer spin particles) and bosons (integer spin particles) It can be viewed as a space-time extension of the Poincare (Lorentz plus translational invariance) group, involving new anticommuting dimensions. We will study elliptic Calabi-Yau manifolds which in addition admit a K3 fibration; in other words we consider the case where the K3 fiber itself is elliptically fibered This would be useful for dualities with heterotic strings. There is a natural sequence of group embeddings which gives the Minimal Supersymmetric Standard Model gauge group and matter structure that can be detected at the LHC [5]

Reflexive Polyhedra as Geometric Realization of Calabi-Yau Fourfolds

Nesting of polyhedra

Conclusions