Coset Construction Research Articles

Aspects of a lagrangian formulation for modular invariant co-set constructions

We discuss the quantum equivalence between a special class of gauaged conformal theories and modular invariant co-set constructions. We emphasize the lagrangian formulation of the C < 1 discrete series

G/H conformal field theory from gauged WZW model

We show that the coset construction for affine algebras ĝ ⊃ ĥ can be realized by coupling a group G WZW model to a gauge field taking values in the Lie algebra h. The partition function of the coset models is computed exactly in terms of the branching functions of ĝ⊃ĥ. Correlation functions may be expressed in terms of those of the G-valued WZW model and of the H scc/H-valued one, also exactly soluble. The special cases include unitary, superconformal, paramefermionic and other discrete series.

Cosmological string theories and discrete inflation

We catalogue string theories which can be interpreted as Robertson-Walker cosmologies. In the absence of dynamic matter, we find only two discrete classes of such theories: static Einstein universes and linearly expanding Milne universes. These correspond to conformal field theories on group manifolds, with the sizes of the Einstein universes related to the level of the Kac-Moody algebra, and Milne universes also offering a geometrical interpretation of a Goddard-Kent-Olive coset construction. String loop effects or non-perturbative phenomena can generate a non-trivial dilaton potential, in which case string theory admits an inflationary cosmology whose Hubble constant is related to the gauge coupling. Presently known conformal field theories permit only a discrete set of values for the Hubble constant, all of which are O(1) in Planck units.

Unitary construction of extended conformal algebras

Particular examples and the general structure of extended conformal symmetries in coset conformal field theories are discussed. Discrete series of unitary representations, whose existence had been previously conjectured, are constructed for a class of extended conformal algebras introduced by Fateev and Zamolodchikov (FZ). The construction is a generalisation of the coset construction of the discrete series for the superconformal algebra using the coset spaces so(N) ⊕ su(N)/so(N), for fixed N. The N = 3 series is the FZ S3 algebra and the N = 4 series consists of two commuting copies of the superconformal algebra. A general method for analysing the extended conformal symmetries present in a particular coset theory and of constructing discrete series of representations of extended symmetry algebras is outlined.

AN INFINITE CLASS OF NEW CONFORMAL FIELD THEORIES WITH EXTENDED ALGEBRAS

A large class of 2D conformal field theories with extended Virasoro algebras related to the GKO construction on the coset SU(2)⊗SU(2)/SU(2) is introduced. Through a Feigin-Fuchs construction the Kac formula is deduced. Characters of the highest-weight irreducible representations are given in terms of the GKO decomposition branching functions. Modular invariant partition functions are constructed and an A-D-E classification based on a triple of simply-laced Lie algebras is analyzed in detail.

MODULAR INVARIANCE IN S3 SYMMETRIC 2D CONFORMAL FIELD THEORIES

Using GKO construction, we conjecture a formula for the characters of highest weight irreducible representations of the algebra of conformal models having S3 symmetry with spin 4/3 parafermionic currents constructed by Fateev and Zamolodchikov. The modular transformations of these characters are given and modular invariant partition functions are classified. It turns out that an A-D-E classification similar to that found in conformal and N=1 superconformal theories holds. For the particular case of the tricritical 3-state Potts model the connection with Virasoro characters is given.

Generalized Coulomb-gas formalism for two dimensional critical models based on SU(2) coset construction

Conformal theories associated with the coset construction SU(2) k ×SU(2) l /SU(2) k+ l are described by a generalized Coulomb-gas formalism. An integrable lattice model obtained by k fusions of the 6-vertex model has a continuous critical line containing the level- k Wess-Zumino-Witten model. Its continuum limit is described by tensor products of the parafermionic and free bosonic sectors. Modification of its boundary conditions by the introduction of floating charges, yields the coset models. The discussion extends to non-unitary models. Special attention is paid to the case k = 2, corresponding to N = 1 supersymmetry.

Free field presentation of the A n coset models on the torus

Partition functions of a family of conformal invariant models obtained through the Goddard-Kent-Olive coset construction A n (1) + A n (1)/A n (1) are expressed in terms of a Gaussian free field with magnetic defects on the torus. It is argued that the same relation holds for the corresponding solvable IRF lattice models (where the role of the free field is played by the underlying vertex model with Z n + 1 symmetry).

Coset construction for extended Virasoro algebras

We discuss extensions of the Virasoro algebra obtained by generalizing the Sugawara construction to the higher order Casimir invariants of a Lie algebra g . We generalize the GKO coset construction to the dimension-3 operator for g = A N−1 and recover results of Fateev and Zamolodchikov if N = 3. Branching rules and generalizations to all simple, simply-laced g are discussed.

Automorphic properties of local height probabilities for integrable solid-on-solid models.

The local height probabilities of a class of integrable solid-on-solid models are obtained in terms of the modular forms describing irreducible decompositions of tensor products of ${A}_{1}^{(1)}$ modules. Their critical exponents agree with those of a coset construction of Goddard-Kent-Olive with c not necessarily less than 1.

Radiation damping in classical electrodynamics: Ted Clay Bradbury. Los Angeles State College, Los Angeles, California

Operator quantization of the WZNW theory invariant with respect to an affine Lie algebra ĝ with a constrained û(1)d subalgebra is performed using Dirac's procedure. Upon quantization the initial energy-momentum tensor is replaced by the g/u(1)d coset construction. The sû(2) WZNW theory with a constrained û(1) current is equivalent to the su(2)/u(1) conformal field theory.