Nonlinear Sigma Model Coupled to a Broken Supergravity

Abstract

Nonlinear sigma models are widely expected to play an important role at some underlying level in elementary particle physics. The nonlinear sigma model is easily generalized supersymmetric and can be coupled to supergravity.l) In many phenomenologically consistent supergravity models, the local supersymmetry (SUSY) is assumed to be broken in a hidden sector that interacts with the observable sector (quarks, leptons, ... ) only gravitationally.3) However, it is not evident whether one can construct a supergravity-coupled nonlinear sigma model when the SUSY is broken in the hidden sector. In the present paper, we study a nonlinear sigma model coupled to s1,1pergravity with the SUSY breaking mechanism mentioned above. We find that a class of 1 non-minimal SUSY extensions of the nonlinear sigma model 5),6) can be coupled to the ; broken supergravity. As an application, we show that our method is used as a model for a Higgs sector of Weinberg-Salam model, in which the SU(2) x U(l) gauge symmetry is spontaneously broken at the tree level*) for a certain range of parameters. A global supersYl1l1metric nonlinear sigma model with N scalar superfields ([Ji, U=T1, 2, ',N) is characterized by a Kahler potential K( ([Ji, ([Jj*). The SUf)erspace laglfangian is given by