Dimensional reduction on multiply connected homogeneous spaces

Abstract

We study the dimensional reduction of a gauge theory determined in a (4fd)-dimensional space to the space M ' @ S / R in the case when S / R is a multiply connected homogeneous compact ddimensional space. A classification of all possible multiply connected homogeneous spaces S / R is given and their maximum nonconnectedness groups are determined. The corresponding breaking of the gauge symmetry which is a generalization of the standard scheme of dimensional reduction on coset spaces and of the Hosotani mechanism is investigated.

Dimensional Reduction over Coset Spaces and Supersymmetry Breaking

“…This possibility can be realized due the presence of non-trivial background gauge configurations which are introduced by the CSDR constructions [34], (ii) The possibility to deform the metric of certain non-symmetric coset spaces and thereby obtain more than one scales [23,2,35], (iii) The possibility to use coset spaces, which are multiply connected. This can be achieved by exploiting the discrete symmetries of the S/R [36,2]. Then one might introduce topologically non-trivial gauge field [37] configu-rations with vanishing field strength and induce additional breaking of the gauge symmetry.…”

Dimensional Reduction of N=1, E_8 SYM over SU(3)/U(1) x U(1) x Z_3 and its four-dimensional effective action.

“…We will employ the Wilson flux breaking mechanism [51,52,53]. Let us briefly recall the Wilson flux mechanism for breaking spontaneously a gauge theory.…”

Διαστατική Ελάττωση Υπερσυμμετρικών Θεωριών Βαθμίδας

“…The discrete symmetries F S/R , which act freely on coset spaces B 0 = S/R are the center of S, Z(S) and the W = W S /W R , with W S and mathrmW R being the Weyl groups of S and R, respectively [18,24,55,56]. The freely acting discrete symmetries, F S/R , of the specific six-dimensional coset spaces under discussion are listed in the second and third column of tables 2.1 and 2.2.…”