On Geometrical Interpretation of Non-Abelian Flat Direction Constraints

Abstract

In order to produce a low energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called flat directions, leaving the F- and D-terms of the scalar potential to be zero. The situation becomes particularly interesting when one attempts to realize such directions while assigning VEVS to fields transforming under non-Abelian representations of the gauge group. Since the expectation value is now shared among multiple components of a field, satisfaction of flatness becomes an inherently geometrical problem in the group space. Furthermore, the possibility emerges that a single seemingly dangerous F-term might experience a self-cancellation among its components. The hope exists that the geometric language can provide an intuitive and immediate recognition of when the D and F conditions are simultaneously compatible, as well as a powerful tool for their comprehensive classification. This is the avenue explored in this paper, and applied to the cases of SU(2) and SO(2N), relevant respectively to previous attempts at reproducing the MSSM and the flipped SU(5) GUT. Geometrical interpretation of non-Abelian flat directions finds application to M-theory through the recent conjecture of equivalence between D-term strings and wrapped D-branes of Type II theory. Knowledge of the geometry of the flat direction "landscape" of a D-term string model could yield information about the dual brane model. It is hoped that the techniques encountered will be of benefit in extending the viability of the quasi-realistic phenomenologies already developed.

arXiv comment36 Pages

References in corpus (17)

• Strong Coupling Expansion Of Calabi-Yau Compactification
• Fayet-Iliopoulos Terms in Supergravity and Cosmology
• Varieties of vacua in classical supersymmetric gauge theories
• The Search for a realistic flipped SU(5) string model
• Charged-Lepton-Flavour Violation in the Light of the Super-Kamiokande Data
• Generation Mass Hierarchy in Superstring Derived Models
• Cabibbo--Kobayashi--Maskawa Mixing in Superstring Derived Standard--like Models
• A Minimal Superstring Standard Model II: A Phenomenological Study
• A Minimal Superstring Standard Model I: Flat Directions
• Non-Abelian Flat Directions in a Minimal Superstring Standard Model
• Phenomenology of Non-Abelian Flat Directions in a Minimal Superstring Standard Model
• Cabibbo Mixing in Superstring Derived Standard--like Models
• Precision prediction of gauge couplings and the profile of a string theory
• Fermion Mass Textures in an M-Inspired Flipped SU(5) Model Derived from String
• On the Possibility of Optical Unification in Heterotic Strings
• Flat Directions in Flipped SU(5) I: All-Order Analysis
• Higgs Mass Textures in Flipped SU(5)