Coset space dimensional reduction and classification of semi‐realistic particle physics models

Abstract

Starting from a Yang‐Mills‐Dirac theory defined in ten dimensions we classify the semi‐realistic particle physics models resulting from their Forgacs‐Manton dimensional reduction. The higher‐dimensional gauge group is chosen to be E8. This choice as well as the dimensionality of the space‐time is suggested by the heterotic string theory. Furthermore, we assume that the space‐time on which the theory is defined can be written in the compactified form M4 × B, with M4 the ordinary Minkowski spacetime and B = S/R a 6 ‐ dim homogeneous coset space. We constrain our investigation in those cases where the dimensional reduction leads in four dimensions to phenomenologically interesting and anomaly‐free GUTs such as E6, SO(10) and SU(5). However the four‐dimensional surviving scalars transform in the fundamental of the resulting gauge group are not suitable for the superstrong symmetry breaking of the Standard Model. The main objective of our work is the investigation to which extent the latter can be achieved by employing the Wilson flux breaking mechanism.

Coset Space Dimensional Reduction and Wilson Flux Breaking of Ten-Dimensional N=1, E(8) Gauge Theory

“…In the present work, starting with a supersymmetric N = 1, E 8 gauge theory in ten dimensions we made a complete classification of the models obtained in four dimensions after reducing the theory over all multiply connected six-dimensional coset spaces, resulting by moding out all the freely acting discrete symmetries on these manifolds, and using the Wilson flux breaking mechanism in an exhaustive way. The results of our extended investigation have been partially presented in a short communication [58]. Despite some partial success, our result is that the two mechanisms used to break the gauge symmetry, i.e.…”

Noncommutative geometry of phase space

“…Over the passed few years a noncommutative generalization of the Cartan frame formalism has been developed [2,3] and applied [4][5][6][7] with varying degrees of success to problems in gravitational physics, notably to the possibility of blowing up [8] the Big Bang. One distinguishing feature of this formalism is that the field equations are not derived from an action principle but rather from constraints imposed on the frame arising from Jacobi identities.…”

Noncommutative geometry of phase space

“…Over the passed few years a noncommutative generalization of the Cartan frame formalism has been developed [3,4] and applied [5,6,7,8] with varying degrees of success to problems in gravitational physics, notably to the possibility of blowing up [9] the Big Bang. One distinguishing feature of this formalism is that the field equations are not derived from an action principle but rather from constraints imposed on the frame arising from Jacobi identities.…”