Vacuum expectation values of Higgs scalars in aSU(2)L×SU(2)R×U(1)gauge model

1979 ◽  
Vol 19 (5) ◽  
pp. 1601-1604
Author(s):  
T. Kitazoe ◽  
G. B. Mainland ◽  
K. Tanaka
Keyword(s):  
Vacuum Expectation ◽  
Gauge Model ◽  
Expectation Values

Gauge hierarchies for chiral SU(N) × SU(N) groups

1976 ◽  
Vol 54 (16) ◽  
pp. 1660-1663 ◽  
Author(s):  
Shalom Eliezer
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Gauge Theories ◽  
Vacuum Expectation ◽  
Coupling Constants ◽  
Spontaneous Breaking ◽  
Text Representation ◽  
Algebraic Equations ◽  
Expectation Values ◽  
Special Case

We have presented a special case where a hierarchy of spontaneous breaking of the symmetries can be achieved in conventional gauge theories (i.e. the Higgs scalars are elementary bosons and the coupling constants of the quartic interactions are small). We break spontaneously the chiral group SU(N) × SU(N) with Higgs scalars transforming like the (N, [Formula: see text]) representation of SU(N) × SU(N). By minimizing the potential we obtain a set of algebraic equations of the type[Formula: see text]where ηj are the vacuum expectation values of the Higgs scalars and μi2 and Aij are parameters. In order to get a hierarchy of spontaneous symmetry breaking we obtain the condition det Aij = 0.

scholarly journals MINIMAL SUPERSTRING STANDARD MODEL: A REVIEW

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 949-951 ◽  
Author(s):  
Gerald B. Cleaver
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Gauge Group ◽  
Effective Field Theory ◽  
Vacuum Expectation ◽  
Effective Field ◽  
Heterotic String ◽  
Expectation Values ◽  
String Solution

I review a heterotic-string solution in which the observable sector effective field theory just below the string scale reduces to that of the MSSM, with the standard observable gauge group being just SU(3)C × SU(2)L × U(1)Y and the SU(3)C × SU(2)L × U(1)Y - charged spectrum of the observable sector consisting solely of the MSSM spectrum. Associated with this model is a set of distinct flat directions of vacuum expectation values (VEVs) of fields that all produce solely the MSSM spectrum. Some of these directions only involve VEVs of non-Abelian singlet fields while others also contain VEVs of non-Abelian charged fields. The phenomenology of theses flat directions is summarized.

scholarly journals ON GEOMETRICAL INTERPRETATION OF NON-ABELIAN FLAT DIRECTION CONSTRAINTS

2008 ◽  
Vol 23 (22) ◽  
pp. 3461-3492 ◽  
Author(s):  
G. B. CLEAVER ◽  
D. V. NANOPOULOS ◽  
J. T. PERKINS ◽  
J. W. WALKER
Keyword(s):  
Scalar Potential ◽  
String Model ◽  
Vacuum Expectation ◽  
Vacuum State ◽  
Effective Field ◽  
Geometrical Interpretation ◽  
Expectation Values ◽  
Brane Model ◽  
Yield Information ◽  
Comprehensive Classification

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 vacuum expectation values 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.1 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 quasirealistic phenomenologies already developed.

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