N = 1 superspace formulation of N = 2 and N = 4 super-Yang-Mills models with central charge

The component models of N = 2 and N = 4 supersymmetric Yang-Mills theories of Sohnius, Stelle and West are reformulated in terms of N = 1 superfields. The non-supersymmetric constraints are supersymmetrized generalizing the linear multiplet in the presence of the non-abelian gauge superfield and (in the N = 4 case) a doublet of chiral superfields. The extended supersymmetry transformations preserving constraints are explicitly given in terms of N = 1 superfields. We are able to introduce the constraints back into the lagrangian using superfield Lagrange multipliers. The on-shell equivalence of this formulation with the formulation of Fayet with one (for N = 2) and three (for N = 4) chiral superfields is shown. The abelian N = 2 model is worked out to show the connection between full superspace treatment and the N = 1 superfield formulation.     

Linearized N = 2 superfield supergravity

We present the formulation of linearized SU(2) supergravity and U(2) conformal supergravity in terms of unconstrained N = 2 superfields: the gauge superfield, compensating superfields, gauge transformations, supertensors, actions and covariant derivatives.     

Superprojectors

We present a simple algorithm for constructing the N-extended superfield projection operators for irreducible representations of supersymmetry, and explicitly perform all simplifications due to spinor derivative algebra. The method is based on covariant expansion of a general superfield in terms of chiral superfields, and requires no knowledge of Casimir operators. We list these superprojectors for various N = 1, 2, and 4 superfields, and apply our results to quantized the linearized N = 2 vector multiplet in a supersymmetric gauge.     

Scale invariant d = 10 superspace and the heterotic string

The superspace formulation of the d = 10 Einstein-Yang-Mills system is presented. Our torsion constraints imply that the solution of the Bianchi identities will be expressed in terms of fields appearing naturally in the heterotic string. The scaling properties of superspace allow a formulation with all superfields dimensionless as well as one with superfields of canonical dimensions. The dimensionless formulation gives rise to a set of very simple supersymmetry transformation rules. This approach may facilitate the investigation of the effects of introducing string-induced higher derivative terms.     

Green functions in a super self-dual Yang-Mills background

In euclidean supersymmetric theories of chiral superfields and vector superfields coupled to a super-self-dual Yang-Mills background, we define Green functions for the Laplace-type differential operators which are obtained from the quadratic part of the action. These Green functions are expressed in terms of the Green function on the space of right chiral superfields, and an explicit expression for the right chiral Green function in the fundamental representation of an SU(n) gauge group is presented using the supersymmetric version of the ADHM formalism. The superfield kernels associated with the Laplace-type operators are used to obtain the one-loop quantum corrections to the super-self-dual Yang-Mills action, and also to provide a superfield version of the super-index theorems for the components of chiral superfields in a self-dual background.     

Ten-dimensional supersymmetric Yang-Mills theory in terms of four-dimensional superfields

We show that the usual formulation of the N = 4 supersymmetric Yang-Mills theory in terms of N = 1 superfields can be generalized to describe the full ten-dimensional theory.     

Left chiral “zero modes” in a super-self-dual Yang-Mills background

A super-self-duality constraint can be imposed on the curvature two-form in supersymmetric Yang-Mills theories formulated in euclidean superspace. If left covariantly chiral superfields are coupled to such a background, part of this space of superfields is annihilated by a superspace operator constructed from the quadratic part of the action. These are analogous to the zero modes of the Dirac equation which occur in the presence of a multi-instanton. Using the supersymmetric version of the ADHM formalism, this space of left covariantly chiral “zero mode” superfields is constructed in the fundamental representation of an SU(n) gauge group. It is shown to be spanned by a set of k superfields, where k is the instanton number of the bosonic component of the Yang-Mills background.     

Superfield formulation of the N=2 super-Yang-Mills model with central charge

The N = 2 super-Yang-Mills model with central charge is constructed in terms of the N = 1 superfields. The supersymmetric constraints generalizing the linear multiplet in the non-abelian case are found. This formulation is shown to be equivalent, using the supersymmetric Lagrange multipliers, to the previously known formulation of Fayet.     

Goldstino and sgoldstino in microscopic models and the constrained superfields formalism

We examine the exact relation between the superconformal symmetry breaking chiral superfield (X) and the goldstino superfield in microscopic models of an arbitrary Kahler potential (K) and in the presence of matter fields. We investigate the decoupling of the massive sgoldstino and scalar matter fields and the offshell/onshell-SUSY expressions of their superfields in terms of the fermions composites. For general K of two superfields, we study the properties of the superfield X after integrating out these scalar fields, to show that in the infrared it satisfies (offshell) the condition X³=0 and X²≠0. We then compare our results to those of the well-known method of constrained superfields discussed in the literature, based on the conjecture X²=0. Our results can be used in applications, to couple offshell the (s)goldstino fields to realistic models such as the MSSM.     

N = 4 Yang-Mills theory on the light cone

The 10-dimensional supersymmetric Yang-Mills theory is constructed in the light-cone gauge. When the theory is dimensionally reduced to four dimensions it is shown that the corresponding N = 4 theory is conveniently described in terms of a scalar superfield. This formalism avoids the problem of auxiliary fields but is Lorentz invariant only on the mass shell. Similar formalisms in terms of scalar superfields are also sketched for the other supersymmetric Yang-Mills as well as for N = 8 supergravity.     

Stochastic quantization of supersymmetric field theory

The Parisi-Wu stochastic quantization method is applied to supersymmetric field theory. The Langevin equation, which reproduces the Green functions of euclidean field theory, is written in terms of superfields. Supersymmetric U(1) theory under gauge fixing and the large N reduction in chiral SU(N) theory are discussed. Regularization based on the stochastic method is studied also.     

Decomposition of extended superfields into irreducible representations of supersymmetry

We give the decomposition of superfields with arbitrary Lorebtz and U(N) indices, in terms of irreducible representations of N extended [including U(N)] supersymmetry. The spectra of the superspin and super-U(N) Casimir operators as well as one missing label operator are given in closed form.     

N=1 supergravity theories coupled to matter and duality transformations

The most general action for chiral and complex linear superfields coupled to theN=1 old minimal supergravity is given. Scalar potentials for pure complex linear and mixed cases are found. A condition for the breakdown of the duality transformation, which transforms a theory with complex linear superfields to one with chiral scalar superfields, is obtained. When this condition is satisfied, the potentials and couplings cannot be transformed, in general, into a Kähler form; examples are given. Some aspects of vanishing cosmological constant are considered in this context.     

Supergravity supergraphs

We describe perturbation theory for supergravity in terms of superfields, using globally-supersymmetric gauge-breaking terms. In the more convinient gauges, the supergravity superfields are a real four-vector and a chiral scalar.     

Linearized N=2 Poincaré supergravity in terms of SU(2)-extended superfields

Linearized Poincaré N=2 supergravity is presented in terms of SU(2)-extended superfields. Thus, the connection of SU(2)-extended superfields with the structure of auxiliary fields in N=2 supergravity is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 31–34, October, 1986.     

Superfield currents of PoincaréN=1 supersymmetry

Starting from the algebraically reduced PoincaréN=1 superspace Noether-current, represented by four superfields obeying a conservation law, the question of further reductions is investigated. Each reduction is defined by a transformation of the four superfields leaving the conservation law as well as certain superfield currents built from them invariant. Two requirements for these superfield currents are stated and the corresponding equations are solved. An additional requirement related to, the uniqueness of the component currents is postulated.     

The structure of the new superspace

The new superspace of Wess and Zumino is generalized to the unconstrainedN-extendedD-dimensional case, it amounts actually to a reparametrization of the old superspace. Recurrence relations for the transformation law and for the covariant derivatives of the superfields defined in the new superspace are obtained. The definition of the component fields as local Lorentz covariant fields has the consequence that the gauge covariant expressions obtained for the vielbein and the connection of the new superspace don't contain the terms dropped out in the Wess-Zumino gauge of supergravity.     

Representations of N = 4 supersymmetry on superfields

We determine all of the irreducible representations (irreps) of the extended supersymmetry algebra (for N = 2 and 4) on superfields with arbitrary external spin in terms of the associated eigenvalues of suitable Casimirs of enlarged algebras. Detailed results are presented for the scalar, spinor and vector superfield cases. The component content of the corresponding irreps are also discussed by means of suitable basis functions.     

Duality transformation and non-Kähler couplings and potentials in anN=1 supergravity theory

A condition for the breakdown of the duality transformation to transform a theory with complex linear superfields to the one with chiral scalar superfields is obtained, when coupled to theN-1 old minimal supergravity multiplet. The recently constructedN=1 supergravity theory, with multiple compensators coupled to a chiral scalar matter supper-field, which has non-Kähler couplings and potential, satisfies this condition. We also indicate other ways of satisfying this condition.