The unitary constructions of the N=4 SU (2) extended superconformal algebras

Unitary conditions for the N=4 SU (2) extended superconformal algebras (SUCAs) are derived. All highest weight unitary representations are identified and explicitly realized by free fermion and (twisted) boson constructions, which are essentially free theories.     

On the geometric interpretation of N = 2 superconformal theories

We clarify certain important issues relevant for the geometric interpretation of a large class of N= 2 superconformal theories. By fully exploiting the phase structure of these theories (discovered in earlier works) we are able to clearly identify their geometric content. One application is to present a simple and natural resolution to the question of what constitutes the mirror of a rigid Calabi-Yau manifold. We also discuss some other models with unusual phase diagrams that highlight some subtle features regarding the geometric content of conformal theories.     

Lattice models in statistical mechanics for N = 2 superconformal field theory

We study exactly solvable cyclic solid-on-solid models extended to arbitrary higher degrees of the fusion construction. A detailed calculation of their local state probabilities via the corner transfer matrix method is presented. The order parameters thus obtained include new characters of the conformal field theories. We discuss a series of lattice analogues of the N = 2 superconformal minimal models included in this family of the cyclic solid-on-solid models.     

On the Poisson-Lie T-duality in two-dimensional N=2 superconformal field theories

A supersymmetric generalization of the Poisson-Lie T-duality transformation is proposed. It is shown that N=2 superconformal two-dimensional WZNW models possess natural Poisson-Lie symmetry, which makes it possible to construct Poisson-Lie T-dual σ models. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 12, 823–828 (25 December 1996)     

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.     

Highest weight representations of the N = 3 superconformal algebras and their determinant formulae

The highest weight representations of the periodic and antiperiodic N = 3 superconformal algebras in two dimensions are described. Determinant formulae for these representations are conjectured. Supercharacters for the periodic N = 3 algebra are defined, and their relationship to the standard characters explained. The physical applications are discussed.     

Wilson loops in $ mathcal{N} = 2 $ superconformal Yang-Mills theory

We study the problem of imposing Dirichlet-like boundary conditions along a static spatial curve, in a planar Noncommutative Quantum Field Theory model.

After constructing interaction terms that impose the boundary conditions, we discuss their implementation at the level of an interacting theory, with a focus on their physical consequences, and the symmetries they preserve. We also derive the effect they have on certain observables, like the Casimir energies.

     

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.     

Modular invariance in N=2 superconformal field theories

The modular invariance properties of two-dimensional N=2 superconformal field theories are studied. It is shown that the character formulae of the central charge c<3 unitary highest weight representation for the untwisted algebras can be written in terms of the string functions and the theta functions of the affine su(2) Kac-Moody algebra. Deriving the modular transformation of the characters we construct the modular invariant partition functions on a torus. The character relation corresponding to the coset space construction of the unitary discrete series in the N=2 algebra is also obtained.     

Effective lagrangian for spontaneously broken N = 2 superconformal symmetry

In a general framework of non-linear realizations for space-time symmetries, we investigate the effective lagrangian for N = 2 superconformal symmetry which is spontaneously broken down to N = 2 super-Poincaré symmetry. For the case in which the dilation multiplet is a massless N = 2 gauge multiplet, we derive a low-energy effective lagrangian which describes the interaction of Nambu-Goldstone particles.     

On the classification ofN=2 superconformal coset theories

We show that two dimensionalN=2 superconformal field theories cannot be constructed by applying the supersymmetric extension of the GKO construction to the so-called special subalgebras, i.e. subalgebras for which at least one generator associated to a root of the subalgebra does not correspond to a root of the algebra itself. We thus prove the completeness of the classification ofN=2 supersymmetric coset models obtained by Kazama and Suzuki. Furthermore we point out that compared to their papers an additional criterion has to be added in theN=2 conditions.     

Heterotic string compactification on N = 2 superconformal theories with c = 9

We study (2, 2) compactifications of the heterotic string by tensoring the discrete N = 2 superconformal series. We construct all models with c = 9 that preserve N = 1 spacetime supersymmetry and discuss some of their properties.