Dynamical Symmetry Breaking in Einstein Universe

We investigate four-fermion interactions with N -component fermion in Einstein universe for arbitrary space-time dimensions (2 ≤ D < 4). It is found that the effective potential for composite operator ψψ is calculable in the leading order of the 1/N expansion. The resulting effective potential is analyzed by varying the curvature of the space-time and is found to exhibit the symmetry restoration through the second-order phase transition. The critical curvature at which the dynamical fermion mass disappears is analytically calculated. e-mail : [email protected] e-mail : [email protected] e-mail : [email protected] 1 It is the standard scenario of the cosmology to assume that in the stage of the very early universe the grand unified theory (GUT) branched off into the quantum chromodynamics and electroweak theory through the symmetry breaking caused by the Higgs mechanism. At this stage the quantum effect of the gravity is considered to be unimportant although the curvature effect due to the strong gravity still remains to be of major importance. It is thus of interest to deal with quantum field theory in curved space-time in the era of the grand unified theory. If we take the view of the dynamical symmetry breaking [1] such as the technicolor model [2], the Higgs particle playing an important role in the symmetry breaking in the GUT era is thought of as a composite system of the fundamental fermion and anti-fermion. Hence it is very interesting to discuss quantum field theory with the composite Higgs field in curved space-time [3, 4, 5]. In the present paper we deal with the four-fermion interaction theory as one of the prototypes of the composite Higgs theory. In order to get an insight into the dynamical symmetry breaking through the composite Higgs mechanism we study the phase structure of the four-fermion theory in curved space-time. The four-fermion interaction in curved space-time is characterized by the action S = ∫ dx √−g [ − N ∑ k=1 ψkγ ∇μψk + λ0 2N ( N ∑