A locally supersymmetric and reparametrization invariant action for the spinning string

We construct an action for the spinning string which is locally supersymmetric and reparametrization invariant using the techniques of supergravity. In a special gauge it is shown that the equations of motion and the constraints are those of the Neveu-Schwarz-Ramond model.     

Primordial cosmological inflation versus local supersymmetry breaking in SUSY GUTs coupled toN=1 supergravity

We present a model for a SUSY GUT coupled toN=1 supergravity in which local supersymmetry breaks down in the gauge singlet sector. The constraints for the model to be physically acceptable are incompatible with inflation. The simultaneous breaking of local supersymmetry and gauge symmetry is proposed as a good prospect for inflation.     

Renormalization group equations for softly broken supersymmetry: The most general case

The renormalization group equations are derived for the most general gauge theory with softly broken supersymmetry. When specialized to the case that global supersymmetry breakdown is induced by spontaneously broken supergravity, the results exhibit new features which are important when applied to models which go beyond the simplest standard model with minimal particle content. As an application the renormalization group equations are given for a standard model with four Higgs doublets as well as for the minimal standard model including generation mixing, both in the framework of broken supergravity.     

Supergravity as a gauge theory of supersymmetry

In a new approach to supergravity we consider the gauge theory of the 14-dimensional supersymmetry group. The theory is constructed from 14×4 gauge fields, 4 gauge fields being associated with each of the 14 generators of supersymmetry. The gauge fields corresponding to the 10 generators of the Poincaré subgroup are those normally associated with general relativity, and the gauge fields corresponding to the 4 generators of supersymmetry transformations are identified with a Rarita-Schwinger spinor. The transformation laws of the gauge fields and the Lagrangian of lowest degree are uniquely constructed from the supersymmetry algebra. The resulting action is shown to be invariant under these gauge transformations if the translation associated field strength vanishes. It is shown that the second-order form of the action, which is the same as that previously proposed, is invariant without constraint.     

Spontaneous breaking of supersymmetry and gauge invariance in supergravity

Using the new minimal auxiliary fields of N = 1 supergravity it is found possible to construct a model of local supersymmetry which spontaneously breaks both supersymmetry and gauge invariance. The status of the cosmological constant resulting from this breaking is discussed.     

The Green-Schwarz superstring σ-model

We study the Green-Schwarz superstring coupled to a ten-dimensional supergravity background. We exhibit the background and quantum invariances of the action expanded in terms of normal coordinates. In the presence of nontrivial fermionic background we go to components and identity the vertex operators for emitting the physical supergravity fields. A comparison with the Neveu-Schwarz-Ramond formalism is then obtained by going to light-cone gauge.     

Prototype models for particle structure in gauge supersymmetry

Particle content in prototype models of gauge supersymmetry is examined. The properties of the prototype models which are in common with those of gauge supersymmetries are the initial non-diagonality of the quadratic part of the action, global supersymmetry invariance and the existence of a mass parameter in the quadratic part of the action. The analysis exhibits the particle content of prototype models to consist of normal poles and sets of complex conjugate poles on the physical sheet. Diagonalization of the hamiltonian can be carried out for such systems (in contrast to the prototype model of conformal supergravity where dipole ghosts arose). Essentially the pole structure observed in the prototype models of gauge supersymmetry is the supersymmetric analogue of the Lee-Wick phenomenon where the normal and the complex conjugate poles form global multiplets.     

BRS gauge and ghost field supersymmetry in gravity and supergravity

Becchi-Rouet-Stora transformations are obtained for the following systems: (i) Pure Einstein gravity in first order form with vierbein and spin connection as independent fields. (ii) First order Einstein gravity coupled to Yang-Mills fields. (iii) Pure supergravity. For the first two systems the results are as in Yang-Mills theory. But for conventional supergravity the BRS transformations leave the effective action invariant only if the classical equations of motion are satisfied. New transformations of the gauge fields of supergravity have been proposed under which the supersymmetry algebra closes. The corresponding BRS transformations do leave the effective action invariant without the need to use the classical equation of motion; moreover, as in Yang-Mills theories, they are nilpotent and have unit Jacobian.     

Local supersymmetry for spinning particles

First and second order forms of the covariant action for a spinning particle are exhibited. The action consistently incorporates the necessary constraints and is invariant under both local supersymmetry and general time parameter transformations, and provides a simple one-dimensional model for the interaction between matter and supergravity. A formulation invariant under general co-ordinate transformations in superspace is also given and shown to be equivalent to the locally supersymmetric one.     

Toward a unification of “everything” with gravity

Combining the ideas of gauge interactions with a global supersymmetry, we build a unified model in six dimensions step by step, starting with a single generation of leptons and ending with three generations of leptons and colored quarks forming a supermultiplet characterized by a most general extensionN=8. The puzzle of supersymmetric partners, such as the gravitino, photino, s-leptons, and s-quarks, is seen in a new light. The supersymmetry is only a global one, whereas local supersymmetry and supergravity are replaced by the theory of gauge interactions and by the usual general relativity of Einstein.     

Properties of the covariant formulation of superstring theories

The covariant two-dimensional action principle that describes the dynamics of free superstrings in a Minkowski background is reviewed. Covariant gauge conditions are formulated, which simplify the equations of motion of the superspace coordinates to free equations. In this gauge there are bosonic and fermionic constraints whose generators give a supersymmetric generalization of the Virasoro algebra. As in certain supersymmetric field theories, closure of the algebra requires using the equations of motion. Covariant constrained bracket relations are obtained for the classical theory, but it is very difficult to extend them to quantum mechanical commutation relations. Interaction vertices satisfying supersymmetry and the necessary gauge conditions are constructed. They reduce in a special frame to ones found in earlier work in the light-cone gauge, and then can be interpreted quantum mechanically.     

Constraints and actions in two and three dimensionalN=1 conformal supergravity

We investigate closure of the gauge algebra and constraints inN=1 conformal supergravity in 2 and 3 dimensions. In the 2 dimensional case, contrary to 3 or higher dimensions, some parts of the gauge fields are algebraically unsolvable in the constraint equations on group curvatures. It will be shown that these unsolvable parts are decoupled from the transformation law as well as from the kinetic multiplets. Hence they are absent in the invariant action for matter multiplets coupled to conformal supergravity which is relevant to the old superstrings. Explicit construction of the invariant actions are illustrated for the case of spinning strings and locally supersymmetric σ-models with the Wess-Zumino term.     

Gauge internal symmetry in extended supergravity

Extended supergravity theories with global O(2) and SO(3) internal symmetry have recently been constructed, and a mechanism which implements local O(2) and SO(3) gauge invariance is given here. The introduction of a minimal gauge coupling automatically leads to a $\text{spin}\text{-}\text{3}\text{2}$ mass and a cosmological term in order to preserve local supersymmetry. Local internal symmetry for a $\text{spin}\text{-}\text{3}\text{2}$ field is related to spontaneous breakdown of global supersymmetry. Perturbation theory results which confirm the physical consistency of the system are given.     

Supergravity with one auxiliary spinor

We present an “intermediate” off-shell version of N = 1 supergravity and its tensor calculus. The supergravity multiplet has 16 + 16 field components. The formulation can be constrained to either of the minimal ones with 12 + 12 components, or enlarge by matter couplings to several 20 + 20 component versions. Self-coupled to its own axial gauge submultiplet it leads to spontaneous supersymmetry breaking in the form first discussed by Freedman and to a propagating gauge field.     

Natural constraints for extended superspace

A simple systematic method to derive superspace constraints is presented. Constraints are given for extended supergravity with one- and two-form gauge potentials in four space-time dimensions. The natural constraints lead to equations of motion forN>4 (supergravity), resp.N>2 (gauge potentials). We discuss modifications for higherN. We also discuss modifications of the field strength of the two-form potential to include Chern-Simons three-forms.     

Hidden constants: The θ parameter of QCD and the cosmological constant of N = 8 supergravity

For field theories that include the abelian gauge field A_μν? the field equations allow an arbitrary integration constant, which does not appear in the lagrangian but which does affect the physics. We present two applications: (i) the θ parameter of effective lagrangians for chiral symmetry breaking in QCD, and (ii) the cosmological constant in N = 8 supergravity, which does not require a gauging of the O(8) symmetry, but is rather due to a spontaneous breakdown of supersymmetry.     

One Fermion-Loop Correction and Supersymmetry in the Heterotic String Theory

(2, 0) world-sheet supersymmetry is shown to be one of the necessary conditions for space-time supersymmetry in most cases. Special care is taken to study the cancellation of local Lorentz and gauge anomalies caused by one fermion-loop..My computation shows that local counterterms which simultaneously restore local Lorentz and gauge invariance of the sigma model do not satisfy the criteria of (2, 0) supersymmetry. But local counterterms and the non-local part of one loop effective action are together invariant under the (2, 0) supersymmetry transformation.     

The Parametrization Invariant and Gauge Invariant Effective Actions in Quantum Field Theory

The review of formulation and methods of calculation of the parametrization and gauge invariant effective actions in quantum field theory is given. As an example the Vilkovisky-De Witt Effective action (EA) is studied (this EA is a natural representative of gauge and parametrization invariant EA's). The examples where the use of the standard EA leads to the ambiguity are demonstrated. This happens as the result of dependence of the standard EA upon the choice of gauge condition. These examples are as follows: Coleman-Weinberg potential in the finite theories and symmetry breaking, EA in quantum gravity with matter and d = 5 gauged supergravity, the possibility of spontaneous supersymmetry breaking in N = 1 supergravity and the spontaneous compactification in the multidimensional R²-gravity. In all these cases the one-loop Vilkovisky-De Witt EA is found and therefore the problem of gauge dependence of EA is solved. The dependence of standard EA of composite fields upon the gauge is studied for the general gauge theories. The class of gauge and parametrization invariant EA's of the composite fields is offered.     

Weak scale supersymmetry without weak scale supergravity

It is generally believed that weak scale supersymmetry implies weak scale supergravity, in the sense that the masses of the gravitino and gravitationally coupled moduli have masses below 100 TeV. This Letter presents a realistic framework for supersymmetry breaking in which these masses can be much larger. This solves the cosmological problems of hidden sector models. Supersymmetry breaking is communicated to the visible sector by anomaly-mediated supersymmetry breaking. The framework is compatible with perturbative gauge coupling unification and can be realized either in models of "warped" extra dimensions or in strongly coupled four-dimensional conformal field theories.