Gauge-invariant sigma models in N=2 superspace

We construct a new broad class of gauge-invariant nonlinear sigma models in N=2 superspace. The dimensional reduction of the theories obtained to d=2 leads to N=4 nonlinear sigma models which are devoid of ultraviolet divergence in all orders of perturbation theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 49–53, February, 1989.     

Gauging N = 2 sigma models in harmonic superspace

We construct the general minimal coupling of N = 2 Yang-Mills fields to N = 2 sigma models in flat and curved harmonic superspace. We show that the complete symmetry group of the matter action can always be gauged in curved space. In flat space, we find that the gauging can be blocked by a local obstruction. We give a number of examples based on homogeneous quaternionic spaces and on quaternionic generalizations of the Taub-NUT and Eguchi-Hanson metrics.     

N=2 super Yang-Mills theory in projective superspace

We constructN=2 Yang-Mills theory in projective superspace by exploiting the analogy to Ward's twistor construction of self-dual Yang-Mills fields.Work supported in part by NSF grant No. PHY 85-07627     

Hamiltonian N=2 superfield quantization

We present a superfield construction of Hamiltonian quantization with N=2 supersymmetry generated by two fermionic charges Q^a. As a byproduct of the analysis we also derive a classically localized path integral from two fermionic objects Σ^a that can be viewed as “square roots” of the classical bosonic action under the product of a functional Poisson bracket.     

On-shell and conformal N = 4 supergravity in superspace

We discuss the superspace geometries which are necessary to describe on-shell O(4) and SU(4) supergravity. The relation of central charge field strengths to physical spin-zero fields is exhibited and a “new” O(4) theory is shown to exist. The version of SU(4) supergravity which uses an antisymmetric tensor gauge field is found to require modifications of ordinary superspace. Finally the Poincaré supergeometry which admits the conformal N = 4 supermultiplet is constructed. It is shown that consistency of the Bianchi identities implies the existence of dimension zero auxiliary fields which are components of a non-linear multiplet.     

N = 4 SYM low-energy effective action in N = 4 harmonic superspace

We apply the N = 4 harmonic superspace with USp(4) harmonic variables for describing the N = 4 SYM low-energy effective action. Scale invariance and gauge symmetry fix the leading term in the low-energy effective action uniquely, up to a constant. The value of the remaining constant can be fixed by the topological quantization condition for the Wess-Zumino term which is present in the component structure of this action.     

Unconstrained multiplet inN=2 conformal supergravity

We investigate an unconstrained (general) multiplet inN=2 conformal supergravity. Transformation law, embedding formula and multiplication rule are explicitly presented at the linearized level.     

A construction of N = 2 and centerless N = 4 superconformal fields via affine superalgebras

In this paper we give a new construction of the N = 2 superconformal algebra using currents of the affine superalgebra and free bosonic fields, and also the N = 4 supercomformal algebra without central charge in terms of currents of and free bosonic fields.     

The action of the supersymmetric N = 2 gauge theory in harmonic superspace

We consider a solution of constraints for the analytic representation of the harmonic superfield connection in the N = 2 supersymmetric gauge theory. A simple geometric expression for the action of this theory is obtained in the form of the integral over the N = 2 superspace.     

N = 2 supersymmetric Ward identities and renormalized BRS and anti-BRS operators in harmonic superspace

The quantization ofN = 2 supersymmetric Yang-Mills theory coupled to a Fayet-Sohnius hypermuttiplet is performed in the harmonic superspace, by requiring BRS and anti-BRS invariances. The corresponding Ward identities and the renormalized BRS and anti-BRS symmetries are derived.     

Cohomological methods in conventionalN=2 superspace

The cohomological methods of Girardi, Grimm and Stora are extended to supersymmetric gauge theories formulated in conventionalN=2 superspace.     

N = 1 complex supersymmetric theory in the harmonic superspace

The N = 1 complex supersymmetric algebra is studied using the harmonic techniques. The massless representations and the classification of their field content in terms of SU(2) n-uplets is obtained. The superspace formulation is developed and the U(1) × U(1) gauge supermultiplet is examined. Other features are discussed.     

N = 2 harmonic superspace with central charges and its application to self-interacting massive hypermultiplets

We investigate the structure of the harmonic superspace formalism with central charges for N = 2 supersymmetry, which is applicable to a wide class of N = 2 theories. As a simple application, the Lagrangian for self-interacting N = 2 massive scalar hypermultiplets is constructed in this formalism, and the interactions are explicitly obtained in terms of physical fields in the lowest order in the coupling constant. Although the theory looks highly unrenormalizable, remarkable cancellations take place so that all radiative corrections vanish in the lowest nontrivial order in the coupling constant.     

ClassicalN=1W-superalgebras from Hamiltonian reduction

A combinatorial proof is presented of the fact that the space of supersymmetric Lax operators admits a Poisson structure analogous to the second Gel'fand-Dickey bracket of the generalized KdV hierarchies. This allows us to prove that the space of Lax operators of odd order has a symplectic submanifold-defined by (anty)symmetric operators-which inherits a Poisson structure defining classicalW-superalgebras extending theN=1 supervirasoro algebra. This construction thus yields an infinite series of extended superconformal algebras.Address after October 1991: Physikalisches Institut der Universität Bonn, FRG     

New D = 10, N = 1 superspace supergravity and local symmetries of superstrings

The superspace formulation of new D = 10, N = 1 supergravity is developed. It is shown that the background superspace of the new theory can be coupled to a test superstring in such a way that the local symmetries of the superstring are intact. This formulation necessarily makes use of the Vainberg construction so the action is analogous to the effective action for QCD with the WZW term. The results suggest that the ambiguity between the massless two-form and six-form in the SO(32) or E₈ × E₈ superstring theories can only be resolved by a gauge invariant, Lorentz-covariant formulation of superstring field theory.     

The Hamiltonian structure of the N = 2 supersymmetric GNLS hierarchy

The first two Hamiltonian structures and the recursion operator connecting all evolution systems and Hamiltonian structures of the N = 2 supersymmetric (n, m)-GNLS hierarchy are constructed in terms of N = 2 superfields in two different superfield bases with local evolution equations. Their bosonic limits are studied in detail. New local and nonlocal bosonic and fermionic integrals both for the N = 2 supersymmetric (n, m)-GNLS hierarchy and its bosonic counterparts are derived. As an example, in the n = 1, m = 1 case, the algebra and the symmetry transformations for some of them are worked out and a rich N = 4 supersymmetry structure is uncovered.     

sℓ(2|1) affine algebra is realized in N=2 strings

sℓ(2|1) affine algebra is realized on the world sheet of an N=2 string in a conformal gauge. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 116–1 21 (25 July 1996)