WZNW Theory Research Articles

An Interplay between Super Structures of Base and Target Spaces

We consider gauged super WZNW theories 'which a~e gauge equivalent to the super Toda theories. It is directly shown that they are on-shell equivalent to the constrained WZNW theories proposed recently. The super structures of the base and target spaces are manifest from the beginning and their interplay is easily .recognized in the present formulation.

Quantum equivalence of constrained WZNW and Toda theories

It is shown that the equivalence between constrained Wess-Zumino-Novikov-Witten theories and generalized Toda theories established previously at the classical level is valid also at the quantum level. The point is that the WZNW → Toda reduction of the lagrangian is paralleled by a similar reduction of the path-integral measure.

Super-Toda theory from WZNW theories

We consider constrained Wess-Zumino-Witten theories for certain types of Lie supergroups. It is shown that they are equivalent to the conformal Toda theories with two-dimensional spacetime supersymmetry. Their relevance to Polyakov's induced supergravity is also discussed.

Conformally reduced WZNW theories and two-dimensional gravity

The WZNW theories (for a non-compact form of the gauge groups) are reduced to a series of integrable theories that interpolate between WZNW theories and the corresponding Toda theories. They described a a set WZNW fields in interaction with each other and with a two-dimensional gravitational field. An algorithm for constructing the general solutions, and a formula that relates the Virasoro and Kac-Moody centres of the reduced theories is given, together with a (conformally non-invariant) extension of the reduction to obtain affine Toda theories.

Explicit quantum symmetries of WZNW theories

Following the recent proposal made by Gómez and Sierra for minimal models, we find the explicit quantum group structure of WZNW models, in their Coulomb gas representation. We construct the quantum group generators in the Chevalley basis as operators creating, destroying or counting screening charges, and show that they satisfy all the required properties, in particular the quantum Serre relations. Using duality under reflection about the background charge, we find the irreducible representations and their tensor product. Our results hold for any untwisted Kac-Moody algebra.

Classical r-matrix and exchange algebra in WZNW and Toda theories

It is shown that the fundamental Poisson brackets in the chiral sectors of WZNW theory and its Liouville-Toda reduction are of the r-matrix form. In general, the r-matrix is monodromy dependent, but in the case of A l Lie algebras, and only then, this monodromy dependence can be “gauged away” by choosing appropriate representatives in the conjugacy classes of the monodromy. The resulting non-trivial solution of the classical Yang-Baxter equation is the classical limit of the quantum R-matrix of A l Toda theory found recently by Cremmer and Gervais.

From geometric quantization to conformal field theory

Investigation of 2d conformal field theory in terms of geometric quantization is given. We quantize the so-called model space of the compact Lie group, Virasoro group and Kac-Moody group. In particular, we give a geometrical interpretation of the Virasoro discrete series and explain that this type of geometric quantization reproduces the chiral part of CFT (minimal models, 2d-gravity, WZNW theory). In the appendix we discuss the relation between classical (constant)r-matrices and this geometrical approach.

Path integral quantization of the coadjoint orbits of the virasoro group and 2-d gravity

Geometrical interpretation of the appearance of SL(2, R ) symmetry in the 2-d quantum gravity is given in terms of the theory of the coadjoint orbits of the Virasoro group. Equivalence of the 2-d gravity and the special type of gauged SL(2, R ) WZNW theory is shown.

Liouville and Toda theories as conformally reduced WZNW theories

It is shown that Liouville theory can be regarded as an SL(2, ø) Wess-Zumino-Novikov-Witten theory with conformal invariant constraints and that Polyakov's SL(2, ø) Kac-Moody symmetry of induced two-dimensional gravity is just one side of the WZNW current algebra. Analogously, Toda field theories can be regarded as conformal-invariantly constrained WZNW theories for appropriate (maximally non-compact) groups.

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.