Superconformal Coset Models Research Articles

Kazama-Suzuki models of N = 2 superconformal field theory and Manin triples

Kazama-Suzuki coset models is an interesting class of N=2 supersymmetric models of conformal field theory which are used to build realistic models of superstring in 4 dimensions. We formulate Kazama-Suzuki construction of N=2 superconformal coset models using more general language of Manin triples and represent the corresponding N=2 Virasoro superalgebra currents in explicit form. A correspondence between the Kazama-Suzuki models and Poisson homogeneous spaces is established also.

The symmetry of large $ \mathcal{N} $ = 4 holography

For the proposed duality relating a family of N=4 superconformal coset models to a certain supersymmetric higher spin theory on AdS_3, the asymptotic symmetry algebra of the bulk description is determined. It is shown that, depending on the choice of the boundary charges, one may obtain either the linear or the non-linear superconformal algebra on the boundary. We compare the non-linear version of the asymptotic symmetry algebra with the non-linear coset algebra and find non-trivial agreement in the 't Hooft limit, thus giving strong support for the proposed duality. As a by-product of our analysis we also show that the W_infinity symmetry of the coset theory is broken under the exactly marginal perturbation that preserves the N=4 superconformal algebra.

ADE singularities and coset models

We consider the compactification of the IIA string to (1+1) dimensions on non-compact 4-folds that are ALE fibrations. Supersymmetry requires that the compactification include 4-form fluxes, and a particular class of these models has been argued by Gukov, Vafa and Witten to give rise to a set of perturbed superconformal coset models that also have a Landau-Ginzburg description. We examine all these ADE models in detail, including the exceptional cosets. We identify which perturbations are induced by the deformation of the singularity, and compute the Landau-Ginzburg potentials exactly. We also show how the the Landau-Ginzburg fields and their superpotentials arise from the geometric data of the singularity, and we find that this is most naturally described in terms of non-compact, holomorphic 4-cycles.

The refined elliptic genus and Coulomb gas formulations of N = 2 superconformal coset models

We describe, in some detail, a number of different Coulomb gas formulations of N = 2 superconformal coset models. We also give the mappings between these formulations. The ultimate purpose of this is to show how the Landau-Ginzburg structure of these models can be used to extract the W-generators, and to show how the computation of the elliptic genus can be refined so as to extract very detailed information about the characters of component parts of the model.

Level-Rank Duality of WZW Theories and Isomorphisms of N = 2 Coset Models

Mappings between certain infinite series of N = 2 superconformal coset models are constructed. They make use of level-rank dualities for B, C, and D type WZW theories, which are described in some detail. The WZW level-rank dualities do not constitute isomorphisms of the theories; for example, for B and D type WZW theories only simple current orbits rather than individual primary fields are mapped onto each other. Nevertheless they lead to level-rank dualities of N = 2 coset models that preserve the conformal field theory properties in such a manner that the coset models related by duality are expected to be, in fact, isomorphic as conformal field theories; in particular, the representation of the modular group on the characters and the ground states of the Ramond sector are shown to coincide. The construction also gives some further insight into the nature of the resolution of field identification fixed points of coset theories.

Lattice analogues of N = 2 superconformal models via quantum-group truncation

We obtain lattice models whose continuum limits correspond to N = 2 superconformal coset models. This is done by taking the well-known vertex model whose continuum limit is the G×G/G conformal field theory, and twisting the transfer matrix and modifying the quantum-group truncation. We find that the natural order parameters of the new models are precisely the chiral primary fields. The integrable perturbations of the conformal field theory limit also have natural counterparts in the lattice formulation, and these can be incorporated into an affine quantum-group structure. The topological, twisted N = 2 superconformal models also have lattice analogues, and these emerge as an intermediate part of our analysis.

N=2 SUPERCONFORMAL INTERACTING BOSONIC MODELS

Bosonic representations of N=2 superconformal algebra are studied. We show that the free energy momentum tensor decomposes into an orthogonal sum of the interacting bosonic model (IBM) and a coset-like tensors. We define the notion of flags of models and show that the central charge does not decrease along the flags. We examine the conditions for an arbitrary un-oriented graph to form an IBM. We discuss several properties of the chiral algebra of these models and examine the role of the continuous parameters by studying an example. Finally we discuss the relations between these models and the N=2 superconformal coset models.

On topological -algebra field theories

We show how certain conformal field theories with W-algebraic structure and vanishing central charges can be interpreted as topological field theories, by mapping them to N = 2 superconformal coset models. Appropriate identifications among vacuum states generate non-trivial ring structures for the topological observables.

N = 2 superconformal models and their free field realization

We discuss whether the N = 2 superconformal coset models can be described in terms of free fields by bosonizing directly the currents in the coset models. For this purpose, we develop the N = 2 superfield formalism for the N = 2 supercoset models. It is shown that this N = 2 superfield formulation naturally leads to a simple free field realization (or bosonization) of the supersymmetrized parafermionic models SU(2)/U(1) (the N = 2 minimal models) and SU(3)/U(1) 2. We also discuss various relations between the bosonized forms of the currents in coset models.