Nonlocal current algebra and N = 2 superconformal field theory in two dimensions

We present a new construction of the unitary highest weight representations of the N = 2 superconformal algebras in two dimensions. This construction is based on the non-local current in the Z_N conformal theory and a free scalar field. It provides a physical realization of all the unitary N = 2 superconformal field theories by critical systems. The correlation functions of the theories can be calculated through this construction.     

A newN= 6 superconformal algebra

In this paper we construct a newN = 6 superconformal algebra which extends the Virasoro algebra by theSO ₆ current algebra, by 6 odd primary fields of conformal weight 3/2 and by 10 odd primary fields of conformal weight 1/2. The commutation relations of this algebra, which we will refer to asCK ₆, are represented by short distance operator product expansions (OPE). We constructCK ₆, as a subalgebra of theSO(6) superconformal algebra K₆, thus giving it a natural representation as first order differential operators on the circle withN = 6 extended symmetry. We show thatCK ₆ has no nontrivial central extensions. Partially supported by NSC grant 85-2121-M-006-019 of the ROC. Partially supported by NSF grant DMS-9622870.     

Simple superconformal field theories in two dimensions

Superconformal field theories with first-order lagrangians, the super BC-systems, are considered on an arbitrary Riemann surface with an arbitrary gravitino field. The corresponding functional integrals are carefully defined, and the Weyl, supersymmetry, and holomorphic anomalies are computed. All the anomalies have a common coefficient. The holomorphic anomaly involves terms quadratic in the gravitino field.     

The minimal superconformal (p,0) supercurrents in two dimensions

Superconformal transformations in rigid (p, q) superspace are defined. For the (p, 0) case it is shown how the general superspace Noethercurrent for any given model can be reduced to a minimal supercurrent. This generalization of the energy-momentum tensor consists of two (p, 0) superfields, and the conservation equations show that no auxiliary currents are present in their components.     

Quantum deformedsu(m/n) algebra and superconformal algebra on quantum superspace

We study a deformedsu(m/n) algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed superconformal algebra. From the deformedsu(1/4) algebra, we derive deformed Lorentz, translation of Minkowski space,iso(2, 2) and its supersymmetric algebras as closed subalgebras with consistent automorphisms.     

The Vaidya solution in higher dimensions

The Vaidya metric representing the gravitational field of a radiating star is generalized to spacetimes of dimensions greater than four.     

Determinant formula for the topological N = 2 superconformal algebra

The Kac determinant for the topological N = 2 superconformal algebra is presented as well as a detailed analysis of the singular vectors detected by the roots of the determinants. In addition we identify the standard Verma modules containing ‘no-label’ singular vectors (which are not detected directly by the roots of the determinants). We show that in standard Verma modules there are (at least) four different types of submodules, regarding size and shape. We also review the chiral determinant formula, for chiral Verma modules, adding new insights. Finally we transfer the results obtained to the Verma modules and singular vectors of the Ramond N = 2 algebra, which have been very poorly studied so far. This work clarifies several misconceptions and confusing claims appeared in the literature about the singular vectors, Verma modules and submodules of the topological N = 2 superconformal algebra.     

Analytic expressions for singular vectors of theN=2 superconformal algebra

Using explicit expressions for a class of singular vectors of theN=2 (untwisted) algebra and following the approach of Malikov-Feigin-Fuchs and Kent, we show that the analytically extended Verma modules contain two linearly independent neutral singular vectors at the same grade. We construct this two dimensional space and we identify the singular vectors of the original Verma modules. We show that in some Verma modules these expressions lead to two linearly independent singular vectors which are at the same grade and have the same charge.     

Study of N = 2 superconformal field theories in 4 dimensions

Making use of the exact solutions of the N = 2 supersymmetric gauge theories, we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. SCFTs we have constructed represent universality classes of the 4-dimensional N = 2 SCFTs.     

The generalized Maxwell-Einstein system in higher dimensions

We study some consequences of the generalized Maxwell-Einstein system in higher dimensions. This generalization is such that the Maxwell-type field constructed in an evenn-dimensional space-time preserves the conformal invariance. After dimensional reduction to four dimensions, it gives rise to scalar, electromagnetic and Kalb-Ramond fields. Specifically, we analyse here some compactification processes, including the stability of the final configuration (forn=8), and anisotropic cosmological solutions (forn=6).On leave of absence from: Departamento de Física e Química, Universidade Federal do Espírito Santo, Goiabeiras, Vitória CEP 29000, Espírito Santo, Brazil     

The super-Poincaré algebra and the scalar superfield in ten dimensions

The super-Poincaré algebra in 10 dimensions is examined. The differences with respect to the other cases are pointed out. In particular, the scalar superfield is considered in detail as an example.