Kiyoshi Higashijima

Spontaneous Breaking of Scale Invariance in a Supersymmetric Model

Abstract The phase structure of a large N, O(N) supersymmetric model in three dimensions is studied. Of special interest is the spontaneous breaking of scale invariance which occurs at a fixed value of the coupling constant, λ0=λc=4π. In this phase the bosons and fermions acquire a mass while a Goldstone boson (dilaton) and Goldstone fermion (“dilatino”) are dynamically generated as massless bound states. The absence of renormalization of the dimensionless coupling constant λ0 leaves these Goldstone particles massless.

The recovery of the chiral symmetry in lattice Gross-Neveu model

The recovery of the chiral symmetry is carefully analyzed in the lattice Gross·Neveu model with Wilsons fermion, by using the effective potential obtained in the large N limit. It turns out that we have to introduce two bare coupling constants for four· fermi interactions as well as the bare mass term in order to obtain the chiral symmetric theory in the continuum limit. A method is proposed to extract the genuine order parameter that scales in the continuum limit. .

Dynamical supersymmetry breaking in two-dimensional N = 1 supergravity theories

Abstract We investigate a possible dynamical mechanism for spontaneous supersymmetrybreaking in N = 1 supergravity theories in 1 + 1 space-time dimensions. It will be shown that supersymmetry is never broken at the tree level, but it can be broken for a certain class of models by quantum effects due to trace anomalies of the energy-momentum tensor and the supercurrent.

Effective potential for qq-condensation

Abstract A method to evaluate the short distance contribution to an effective potential for q q-condensation is proposed. Chiral symmetry is shown to break down spontaneously by studying the effective potential in the two-loop approximation.

A Solution to the Goldstein Problem and the Possibility of Dynamical Chiral Symmetry Breaking

Abstract The Goldstein equation is carefully analyzed by introducing a cutoff to clarify the physical meaning of the continuous spectrum. The solution belonging to the continuous spectrum is shown to represent the renormalized vertex function. It is also shown that no cutoff-independent discrete spectrum exists, whereas the cutoff-dependent one does. On the basis of these results, the possibility of the Nambu-Goldstone realization of chiral symmetry is examined in the vector gluon model. The appearance of the Nambu-Goldstone boson seems to be impossible at least in the ladder approximation except for the model of Englert et al.

Spontaneous breakdown of supersymmetry in the O(N)-symmetric Wess-Zumino model in two dimensions

Abstract We discuss a spontaneous breakdown of supersymmetry in the two (one space and one time)-dimensional O( N ) Wess-Zumino model, by computing the effective potential to the leading order in the 1/ N expansion. The massless Nambu-Goldstone fermion appears as a bound state of the fermion and the boson involved. It is shown that there occurs a phase transition between unbroken-and broken-supersymmetry at a critical point of the mass scale which characterizes the renormalized coupling constant.

VERTEX OPERATORS AND NON-ABELIAN BOSONIZATION

Recent devolopments on the study of conformal algebra are discussed. We present some new results on the representation of Virasoro algebra.

Equivalent lagrangians in large N field theories

Abstract The auxiliary field method is generalized to any O (N)-invariant theory with non-polynomial interactions. In non-supersymmetric theories, two lagrangians with and without an auxiliary field are shown to be equivalent to the leading order of the 1/N expansion. In supersymmetric theories, these two lagrangians are equivalent to all orders of the 1/N expansion. The lagrangian with an auxiliary field is solvable in the 1/N expansion.

Spontaneous breakdown of supersymmetry in three dimensions

Abstract By using the effective potential to leading order in the 1 N expansion, spontaneous breakdown supersymmetry (SUSY) in the O( N )-symmetric Wess-Zumino model in three dimensions is discussed. It is shown that spontaneous breakdown of SUSY does not occur if O( N ) symmetry is broken and results similar to the two-dimensional case are obtained if O( N ) symmetry is unbroken. We also present a criterion for SUSY breaking in a wider class of models.

Group Theoretic Analysis of Conformal Invariant Field Theories

Various issues associated with field theoretic realization of conformal symmetry in 2 dimensions are discussed. A method of constructing primary fields for a class of conformal algebras which are based upon level-2 representations of current algebra are presented. Realizations of twisted current algebra are also discussed. 16 refs.