Harmonic Superspace Research Articles

Topological super Yang-Mills theories

We present a manifestly supersymmetric formulation of N=1 and N=2 topological super YM theories in four dimensions. In both cases, we construct the complete quantum action together with its invariance algebra. For N=2 in harmonic superspace this algebra formally coincides with the one of the bosonic thoery in ordinary spacetime.

Finiteness of (4, 4) non-linear σ-models in light-cone harmonic superspace

We present the (4, 4) non-linear σ-model in two spacetime dimensions in light-cone harmonic superspace and it is proved to be ultraviolet finite. The action, though containing half the spinorial degrees of freedom, is manifestly Lorentz covariant and local. Any loop integration within a supergraph is proved to be finite by explicit calculations.

The quantisation of N=3 super-Yang-Mills off-shell in harmonic superspace

The supersymmetric extension of the transverse gauge is found for the harmonic superspace version of N=3 extended super-Yang-Mills. Using this gauge, the N=3 supersymmetric Feynman rules are derived. The explicit form of the propagators is given along with the relevant SU(3)/U(1)*U(1) and SU(3)/SU(2)*U(1) distributions.

NEW CLASSES OF D = 4, N = 2 SUPERSYMMETRIC NONLINEAR σ MODELS

We show that there exists three independent N = 2, harmonic superspaces denoted as [Formula: see text]; [Formula: see text] and (2, 2)+−. These superspaces are in one-to-one correspondence with the three complex structures of the quaternionic body. The underlying supersymmetric nonlinear σ models preserving the SU(2) symmetry are developed. Two of them are described by a neutral hyperkahler potential. New results are obtained.

Covariant quantization of the Green-Schwarz sigma-model

We present the covariant quantization of the Green-Schwarz superstring in a supergravity background. This is achieved by extending the method of Kallosh and Rahmanov for Lorentz-covariant gauge-fixing of the free Green-Schwarz superstring. In the background field method we introduce harmonic fields for the quantum string variables only, thus avoiding the need for harmonic superspace. Our quantization procedure, while keeping Lorentz invariance manifest, does not put undesirable constraints on the background geometry.

Off-shell six-dimensional supergravity in harmonic superspace

A fully off-shell action for N=2, d=6 Poincare supergravity in harmonic superspace is proposed. It consists of the off-shell actions for a scalar multiplet and for a self-dual tensor multiplet in conformal supergravity background. A new mechanism for describing self-dual tensor fields off shell, in which conformal supergravity plays an active role, is found.

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.

Light-cone auxiliary fields for ten-dimensional super Yang-Mills

We consider ten-dimensional super Yang-Mills in the light-cone gauge and define a set of auxiliary fields which close the light-cone super algebra off-shell. As a necessary preliminary we give a systematic discussion of the auxiliary field problem for simple super Yang-Mills in dimensions 3, 4, 6 and 10 both covariantly and in the light-cone framework. The motivation for this work is that it may prove useful in conjunction with the ideas of harmonic superspace. With this in mind we indicate how the light-cone theory in ten dimensions can be formulated in light-cone superspace using unconstrained superfields.

Generalised Fayet-Sohnius hypermultiplet

The authors present a N=2 harmonic superspace formulation for massless supermultiplets of the type (s-1/2, s, s+1/2), where s is any integer, which generalise the Fayet-Sohnius matter hypermultiplet.

SU(2) classification of N=2 complex supersymmetric representations

The N=2 extended complex supersymmetry representations are constructed. The classification of N=2 multiplets in SU(2) representations is obtained. The relation with N=2 harmonic superspace is also discussed.

General superspaces from supertwistors

The families of composite D=4 N-extended complex superspaces, with 4+ k( N− k) ( k=0, 1, ..., N) bosonic and 4 N fermionic coordinates are obtained from supersymmetric extension of twistor formalism. The description of real superspaces, with real Minkowski coordinates, is also considered. The case N=2, k=1, corresponding to N=2 harmonic superspace of Ogievetski and Sokchaczev, is discussed in some detail.

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 supersymmetric Ward identities on the harmonic superspace

The quantization of N=2 supersymmetric Yang–Mills theory coupled to a matter hypermultiplet has been done in the harmonic superspace by requiring BRS and anti-BRS invariances. The corresponding Ward identities have also been derived.

ON THE HYPERMULTIPLET THEORIES

Using the harmonic superspace techniques, we show that the hypermultiplet [Formula: see text] can be either massive (massless) with or without central charges. We found that the HST hypermultiplet has a degenerate structure. In the case of the absence of central charges, the corresponding mass terms are constructed and they turn out to be similar to those obtained from central charges. A class of infinitesimal duality transformations for free hypermultiplet theory is given.

EXTENDED BRS AND ANTI-BRS SYMMETRIES IN N=2 HARMONIC SUPERSPACE

The full set of extended BRS and anti-BRS symmetries are derived for components of super-connection and gauge superfield using the N=2 harmonic superspace. The quantization of N=2 supersymmetric theory is developed and the proof of its gauge invariance is presented.

New canonical covariant formalism for then N=2, D=10 superparticle

Using a harmonic superspace with new geometry one reduces the N=2, D=10 Brink-Schwarz (BS) superparticle to a covariant system with first-class independent constraints only.

TWO DIMENSIONAL UNTWISTED (4, 4), TWISTED $(4, \bar4)$ AND CHIRAL SUPERSYMMETRIC NON LINEAR σ-MODELS

D=2N=(4, 4) harmonic superspace analysis is developed. The underlying untwisted (4, 4) non linear σ-models are studied. A method of deriving chiral (4, 0) and (0, 4) models is presented. The Lagrange superparameter used to put the constraint specifying the hyperkahler manifold structure is predicted and its relation to the matter superfield is stated in a covariant way. A known construction is recovered. We show also that (4, 4) model is not a direct sum of its chiral ones. Finally a twisted [Formula: see text] model is obtained.

Covariant unconstrained superfield action for the linearized D = 10 super-Yang-Mills theory

A new type of D = 10 harmonic superspace with two generations of harmonics allows us to reduce the D = 10, N = 1 Brink-Schwarz (BS) superpaticle to a system whose constraints are all first class, functionally independent and Lorentz-covariant. Given these properties, the covariant BFV-BRST quantization of the system is straightforward. By second quantizing this system, we circumvent the no-go theorem which forbids the existence of a covariant off-shell unconstrained superfield action for the linearized D = 10 super-Yang-Mills theory.

N=2 SQED model in harmonic superspace

The authors study, in harmonic superspace, the N=2 SQED model based on the interaction of a massive Fayet-Sohnius hypermultiplet and a gauge multiplet. The Fayet-Iliopoulos mechanism is used to break the N=2 SQED model. A general discussion of symmetry breaking is given.

Covariant canonical quantization of the green-schwarz superstring

Introducing a new type of D = 10 harmonic superspace with two generations of harmonic coordinates, we reduce the Green-Schwarz (GS) superstring to a system whose constraints are Lorentz covariant and functionally independent. These features allow us to impose Lorentz-covariant gauge fixing conditions for the reparametrization and the fermionic κ-invariances. The resulting QBRST corresponds to the finite-dimensional Lie algebra of the remaining purely harmonic constraints. The super-Poincaré symmetry acts in a manifestly Lorentz-covariant form and is apparently anomaly free.