Gauged Supersymmetric Generalized Nonlinear Sigma Models for Quarks and Leptons*

We consider the idea of describing quarks and leptons, and their interactions, in terms of gauged supersymmetric generalized nonlinear sigma models. It is found that the best model is the one based on the Kahler manifold E7/sU(4) X U(1)4, with an atipropriate complex structure. The isotropy representation of the manifold is sufficient for embedding three families of quarks and leptons. We as10 discass the problem of the ABJ-anomaly which so frequently occurs in such models. Submitted to Physical Review Letters * Work supported by the Department of Energy, contract DEAC03-76SFOO515. (1) The observed spectrum of quarks and leptons has expanded significantly during --~the last ten years. According to their interactions, the fermions may be grouped into three identical families, with two predicted members, Z+ and t-quark, yet to be contimed by further experiments. In m(3)c X mu X U( 1) unified gauge theory, each fermion family has the representation content (3,s) + 2(3* , 1) + (I, 2) + (I, I), omitting the U( 1) charges. In W(5) grand unified gauge theory, each family is described as 5* + 10. And in SO(l0) gr an d unified gauge theory, it is embedded in the 16 representation. An explanation for the repetition of the family structure is, however, still unavailable. Proceeding to conventional unified gauge theories with bigger gauge groups does not provide a satisfactory answer.’ (2) It is reasonable that the idea of compositeness may be useful somehow for explaining the quark-lepton spectrum. A main theoretical challenge here is that of reconciling the relatively small masses (and in some instances, possibly vanishing masses) of quarks and leptons with the large mass scale2 characterizing the extra strong interactions of the preons (the hypothetical constituents of quarks and leptons). The only analogous situation known in particle physics is that of pions. They are composite and have relatively small masses; the masses are small because of pions’ role as Goldstone particles. Preon models in which massless composite fermions might be produced because of an unbroken chiral symmetry were, and are still, vigorously searched for after ‘t Hooft proposed the anomaly matching condition.’ Disappointingly, a commonly acceptable model of this sort has yet to be found. Another interesting proposal4 is to identify quarks and leptons as composite Goldstone fermions resulting from broken supersymmetries. This approach has the advantage of avoiding questions concerning the nature of preons and their interactions. It requires, however, too many supersymmetries, one for each two-component fermion.