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.     

Modular invariant partition functions for N = 2 superconformal field theories

We find the characters of all the unitary degenerate highest weight representations of the N = 2 superconformal algebras with c<3. The constraints of modular invariance on the field contents of the two-dimensional N = 2 superconformal field theories are explored. The constraints take the form of sum rules on the number of superconformal highest weight representations. Models which satisfy these constraints are classified. We also discuss the condition of unbroken supersymmetry in these models.     

A new approach to spontaneously broken conformal symmetry

In this paper we present a new method for constructing theories of gravitation which exhibit spontaneously broken conformal symmetry. It does not require introducing nongeometric terms (i.e., auxiliary gauge fields or potential terms for the conformal field) into the Lagrangian. It is based on a theory which initially is locally both Lorentz invariant and Weyl gauge invariant inD dimensions. It is shown that, if the field Lagrangian contains terms quadratic in curvature in addition to the Ricci scalar, then the field equations allow both the dilation field and some connection components to have nonvanishing vacuum values. Both Lorentz and Weyl symmetries are thereby broken simultaneously.     

Determinant formulae for the N = 4 superconformal algebras

Determinant formulae for the N = 4 superconformal algebras are conjectured. Comments are made on applications in conformal field theory, string theiry and representation theory, and on the analysis of supersymmetrically extended hyper-Kähler sigma models.     

Impossibility of adding gauge couplings to spontaneously broken N = 8 supergravity

When the four mass parameters of spontaneously broken N = 8 supergravity are taken to be equal, the theory possesses at global SU(4) symmetry. Since it contains massless vectors in the adjoint representation, it is tempting to add gauge interactions so as to make the SU(4) symmetry local. In this paper we show that it is impossible to do this in a way that is consistent with the spontaneous character of the symmetry breaking.     

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 unitary representations of N = 2 superconformal theory

The Kac formula for superconformal dimensions (generalized to N = 2) is further developed (compared to a previous article). A list of discrete values of the central charge for which unitary representations are expected to exist is proposed. For several of these, unitarity is checked by computer. For two values, unitarity is proven by providing explicit fermionic representations. For one of those values, the N = 2 theory coincides with a sub theory of one of the known unitary N = 1 theories, thus extending a similar situation between N = 0 and N = 1.     

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.     

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.     

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.     

Construction ofN = 2 superconformal algebra from affine algebras with extended symmetry: I

The purpose of this Letter is to use the idea of the Sugawara-Ka-Todorov construction of theN = 0 andN = 1 superconformal algebras to construct a very simple free-field realization of theN = 2 superconformal algebra.     

Effective lagrangian and dynamical symmetry breaking in strongly coupled lattice QCD

A method is proposed for computing effective lagrangians in QCD with N colors using lattice regularization. The meson field lagrangian is worked out in detail in the strong coupling limit with various lattice fermion formulations. For generalized Susskind fermions the spontaneous breakdown U(n) ? U(n) → U(n) (diagonal) is found at large N and a generalized version of the non-linear σ model emerges in a natural way. The Nambu-Goldstone spectrum is investigated and a continuous transition is made to Wilson fermions, for which the effective potential and the ππ scattering amplitude are tested on chiral symmetry. Large d (=dimension) approximations are compared with the large N limit and applied to N = 3.     

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)