Standard model gauge group and realistic fermions from the most symmetric cosetM klm

Abstract

A brief survey on Kaluza-Klein theories is given. It is emphasized that for a maximally supersymmetric universe, the only way to do Kaluza-Klein theory is through supergravity. Bearing this in mind, a seven-dimensional internal compact manifold,Mklm,is considered. It is described as being the most general type of coset spaces containing the standard model groupsSU(3) ⊗SU(2) ⊗U(1).Mklmis obtained as a compactification ofD=11 supergravity. It is shown that contary to the manifoldsMpqr,the topology of the spacesMklmis not sensitive to the integers,k, l, m but rather to the 6 parameters that parametrize the subalgebraSU(2) ⊗U(1)′ ⊗U(1)″ taken to be the stability group ofMklm.This gives the spacesMklma much richer topology and thus a much wider class of solutions ofD=11 theory. Also, the most general expressions for the “geometrical” coupling constant are obtained. A consistency condition with the low-energy standard model, with and without supersymmetry, is established. A harmonic expansion analysis is made, it is shown thatMklmmanifold possesses a spinor structure for a given class of parameters. It is shown that for two classes of parametersL 0+ klm andL 0− klm the manifoldMklmbecomes the 8-dimensional coset spaceLklmfor which classes it is seen to be consistent with theSU(3) ⊗SU(2) ⊗U(1) quark and lepton quantum numbers. TheSU(3) ⊗SU(2) ⊗U(1) invariant solutions ofD=11 supergravity are studied. It is shown that all solutions break supersymmetry except for two mirror solutions for whichN=2 supersymmetry is preserved. The 8-dimensional coset manifoldLklmis then considered; it is obtained as a minimal increase on the manifoldMklm.