R. Arnowitt

Superfield densities and action principle in curved superspace

Abstract The concept of determinant is generalized to superspace. Density superfields are defined, and the metric density is obtained. This is used to construct an invariant action principle in curved superspace.

Generalized super-gauge symmetry as a new framework for unified gauge theories

Supersymmetry is generalized to a local gauge invariance. The gauge group unifies electromagnetic (or Yang-Mills) gauge with space-time coordinate invariances. All fields arise from a single gauge superfield. The non-abelian gauge invariance produces self-interactions in the field equations. These automatically generate coupled Maxwell-Dirac, Einstein equations, etc.

Supersymmetric Electroweak Effects on G-2 (mu)

A model independent analysis of the super-symmetric electroweak contribution togμ−2 is discussed within the framework ofN=1 Supergravity unified theory. A detailed comparison with existing experiment of two models (R.G. and T.B.) is carried out. The supersymmetric electro-weak contributions are found to be characteristically different and generally larger than the electro-weak contributions of the standard theory, and in many cases significantly larger. Effects of the hidden sector and the photino mass dependence ofgμ−2 are also investigated. Present data already eliminates some choices of parameters. Reduction of existing experimental errors by a factor of 3 will make contact with most R.G. models and by a factor of 10 with most T.B. models.

Gravity induced symmetry breaking and ground state of local supersymmetric GUTs

Abstract It is shown that local supersymmetry does not necessarily imply existence of anti-de Sitter vacua in grand unified theories. A locally supersymmetric SU(5) grand unified example is presented in which the supergravity interactions make the SU(3) × SU(2) × U(1) vacuum be the absolute minimum of the effective potential for a class of solutions whose Higgs and matter multiplets have no vacuum expectation values in the global limit ( k → 0). Supersymmetry breaking occurs at a scale m s ∼ 1 TeV through super Higgs effect and degeneracy is broken by O ( m s 4 ) rather than O ( K 2 M 6 ).

Supergravity and Gauge Supersymmetry

I would like to talk about the work which Richard Arnowitt and I have done recently regarding the structure of gauge supersymmetry and the relationship of the Riemannian space geometry of gauge super-symmetry to the non-Riemannian superspace geometry of super-gravity1). Rather than start directly with a discussion of the Riemannian geometry of gauge supersymmetry it is perhaps worth while motivating the discussion by recalling the great amount of progress made in the superspace formulations of supergravity2) and the nature of the questions that arise in the framework of such formulations. What the superspace formulations of supergravity show is that supergravity obeys a non-Riemannian geometry in superspace with torsion. The problem which we should like to address ourselves to, however, concerns the amount of unification that occurs in supergravity.

Riemannian geometry in spaces with Grassman coordinates

The use of spaces containing Grassman (anticommuting) coordinates (in addition to the usual space-time coordinates) as a framework for unified gauge theories is described. The theory developed represents a local gauge-invariant extension of conventional (global) supersymmetry. Aside from containing the usual general coordinate invariance group of gravitational theory, the gauge supersymmetry group is seen to also encompass other symmetries of particle physics, e.g., electromagnetic (or Yang-Mills) invariance. The role of spontaneous symmetry breaking and the field equations unifying the Einstein, Maxwell, and Dirac interactions are discussed.

Interaction between gauge vector fields

Abstract The interaction between massless vector fields possessing gauge invariance of the second kind and the Maxwell field is considered. A discussion is given of the special properties of gauge fields and of the definition of minimal electromagnetic coupling. The inconsistency of minimal coupling for the systems in question is reviewed. It is then shown that while a particular non-minimal coupling is consistent for the fields in question, even the latter becomes inconsistent in the presence of other known charged fields. Thus such fields as that of Yang-Mills or the “baryon” gauge field cannot carry charge unless all other charged fields in nature also form appropriate multiplets.

Hard meson analysis of photon decays of πo, η and vectormesons

Abstract A simple derivation of the hard meson result that PCAC and CVC forbid π o , η and vector meson two body, photon decays is given. A model of PCAC breakdown which permits these decays is proposed. The modification PCAC is in agreement with the photon decay data and does not disturb the previous successes of PCAC.

Effective Lagrangians with U(1) axial anomaly I

Abstract The effective lagrangian which includes the U(1) axial anomaly is discussed. The lagrangian describes the interaction of physical mesons of spin-zero and spin-one fields and an effective Kogut-Susskind four-vector anomaly field. The interactions are constructed which satisfy all the anomalous Ward identities for vertices which accommodate arbitrary amounts of chiral and SU(3) symmetry breaking consistent with U(3) × U(3) current algebra.

Superspace formulation of supergravity

Abstract The recent superspace formulations of supergravity using vierbeins are shown to be equivalent to the previous metric tensor superspace formulation of the authors for physical (mass-shell) spaces. An alternate method of gauge completing the vierbein without using Breitenlohner fields is given to the order necessary to generate field equations, and again shown dynamically equivalent to the above formulations.