Nobuyoshi Ohta

Grand Unified Theories Based on Local Supersymmetry

General features are discussed of grand unified theories with local supersymmetry broken at high energies by the super-Higgs effect. The low-energy effective Lagrangian is a globally supersymmetric one with all the explicit soft breakings. It is argued that the energy splittings among the vacua due to gravitational effects must be small in order to be able to pick out the correct vacuum. Also discussed are the mechanisms of breaking SU(2) by the gravitational effects and of suppressing monopole production in the early universe.

The η problem in the large-N limit: Effective Lagrangian approach

Abstract The effective lagrangian for the U(1) problem is reanalysed on the basis of the color gauge invariance of the underlying QCD. The decoupling mechanism of the axial-vector ghost from the physical sector is investigated with a particular gauge-fixing condition. The model is then extended to incorporate flavor degrees of freedom. It is explicitly demonstrated that the suppression mechanism for η →3 π is evaded in a manner consistent with anomalous Ward-Takahashi identities for the U(1) current without massless Nambu-Goldstone boson. The decays of ϑ → η ( η ′) γ are also estimated under the assumption that the decay in question dominantly proceeds through 2 gluons+γ with 2 gluons in the 1 S 0 state. Finally, strong CP violation is briefly discussed.

On the Partial Conservation of the U(1) Current

Recently proposed partial conservation of the UO) current (PCU,C) is applied to estimate the decay rates of various OZI forbidden processes. The results obtained are in good agreement with experiments and thus indicate the important role played by the UO) axial-vector anomaly in these decay processes. Octet jP = } + baryons are next introduced into this scheme and low energy theorems related to the B dependence of the matrix elements are investigated. Physical consequences of non-zero B (strong CP-violation) are also discussed with the help of the PCU,c. The results are used to give the bound on B.

Skew-symmetric tensor gauge field theory dynamically realized in the QCD U(1) channel

Abstract It is shown that, in order for the U(1) Goldstone boson to decouple from the physical sector, a third rank skew-symmetric tensor gauge field theory has to be realized dynamically by asymptotic fields of bound states in QCD. The abelian-like gauge invariance of this tensor gauge theory is just a realization of the original QCD gauge (BRS) invariance which hence assures the decoupling of all the bound-state modes by the “quarlet mechanism”. A general procedure for fixing gauges in such types of skew-symmetric tensor gauge theories is also presented.

Stability of Classical Solutions in Extended {Kaluza-Klein} Theories

Abstract The stability of classical solutions for a scalar field corresponding to the radius of S n = SO( n + 1)/SO( n ) in extended Kaluza-Klein theories is investigated. A stable solution is shown to emerge if an antisymmetric tensor field of rank n −1 or rank-three acquires a nonzero background field strength in S n or in four-dimensional spacetime, respectively.

Dipole mechanism of spontaneous breaking of supersymmetry

Abstract A detailed analysis is given on the method of breaking supersymmetry spontaneously by introducing a supersymmetric dipole field. It is demonstrated how a pair of massless Goldstinos, one with positive metric and the other with negative metric, is decoupled from the physical sector yet results in apparently explicit but soft breaking terms. Due to the presence of an unobservable ghost Goldstino, the vacuum energy is no longer assured to be non-negative in contrast to the usual argument. A dipole of vector multiplets is also proposed to obtain a C -term like breaking without taking a singular limit of the vanishing gauge coupling constant.

On the definitions of γ5 in continuous dimensions

On the basis of a simple model, a demonstration is given to show that the rotational invariance is not restored in the limit N → 4 if the four-dimensional definition γ5 = iγ0γ1γ2γ3 is used in the interaction to calculate higher-order corrections. Also discussed is the implication of the fact that the Adler anomaly occurs for π0 → 12Nγ in the Pauli-Villars regularization method.

Explicit soft versus spontaneous breaking of supersymmetry

Abstract It is shown that all the explicit soft breaking of global supersymmetry are precisely those of the type that may be induced by the spontaneous breaking of supersymmetry. The decoupling mechanism of the accompanying goldstinos from the physical sector is also clarified. Our results provide natural explanations of their softness and strongly suggest that the absence of quadratic divergences leads us uniquely to supersymmetry, either unbroken or broken spontaneously.

Effects of θ in supersymmetric theories

Abstract Possible effects of introduction of the “θ-parameter” into supersymmetric theories are investigated on the basis of a 1/ N expansion. It is found that, in a two-dimensional SU( N )-symmetric U(1) gauge theory without chiral symmetry, supersymmetry remains unbroken in the presence of the θ-term although physical quantities depend on θ and are periodic in θ with period 2π.

Finiteness and supersymmetry breaking due to θ

Abstract It is shown on the basis of 1 n expansion that supersymmetry is spontaneously broken by the “θ-parameter” in a two-dimensional N = 2 supersymmetric model with U(n) symmetry. It is pointed out that this breakdown of supersymmetry is largely due to the finiteness of the theory and that N = 4 supersymmetry in four dimensions will also be broken by the θ-term.