Kareljan Schoutens

W symmetry in conformal field theory

Abstract We review various aspects of W algebra symmetry in two-dimensional conformal field theory and string theory. We pay particular attention to the construction of W algebras through the quantum Drinfeld-Sokolov reduction and through the coset construction.

Extensions of the Virasoro algebra constructed from Kac-Moody algebras using higher order Casimir invariants

Abstract We consider bosonic extensions of the Virasoro algebra that can be obtained from Kac-Moody algebras g by generalizing the Sugawara construction to the higher order Casimirs of g. In this paper we explicitly construct the algebra of a primary field of dimension 3 constructed from the 3rd order Casimir of AN−1. For N = 3 we compare our results to the Z3-extended Virasoro algebra proposed by Fateev and Zamolodchikov.

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.

O(N)-extended superconformal field theory in superspace

Abstract We discuss the superspace formalism for the description of O( N )-extended superconformal quantum field theory in two dimensions. Such theories exist for N ⩽ 4. In O(4)-extended superconformal transformations two independent anomalous terms can be present. Under the assumption that in physical models a specific combination of these anomalies is absent, we show that the allowed values of the N = 4 Virasoro central charge c and c ( n + , n − ) = 6 n + n − /( n + + n − ).

New exactly solvable model of strongly correlated electrons motivated by high-Tc superconductivity

We present a new model describing strongly correlated electrons on a general {ital d}-dimensional lattice. It is an extended Hubbard model and it contains the {ital t}-{ital J} model as a special case. The model naturally describes local electron pairs, which can move coherently at arbitrary momentum. By using an {eta}-pairing mechanism we can construct eigenstates of the Hamiltonian with off-diagonal long-range order. In the attractive case the exact ground state is superconducting in any number of dimensions. On a one-dimensional lattice, the model is exactly solvable by Bethe ansatz.

Off-shell WZW models in extended superspace

Abstract We investigate the off-shell N = 2 and N = 4 structure of the supersymmetric Wess-Zumino-Witten model. We present an off-shell formulation of the SU(2) ⊗U(1) supersymmetric WZW model in terms of N = 2 chiral and twisted chiral multiplets. We show that such a formulation is not possible for any other group and suggest a larger multiplet structure to cover these cases.

Spinon bases, Yangian symmetry and fermionic representations of Virasoro characters in conformal field theory

Abstract We study the description of the SU (2), level k = 1, Wess-Zumino-Witten conformal field theory in terms of the modes of the spin- 1 2 affine primary field φ α . These are shown to satisfy generalized ‘canonical commutations relations’, which we use to construct a basis of Hilbert space in terms of representations of the Yangian Y ( sl 2 ). Using this description, we explicitly derive so-called ‘fermionic representations’ of the Virasoro characters, which were first conjectured by R. Kedem, T. Klassen, B. McCoy and E. Melzer [Phys. Lett. B 307 (1993) 68, and references therein]. We point out that similar results are expected for a wide class of rational conformal field theories.

A new gauge theory for W-type algebras

Abstract The rigid conformal and rigid W3-type symmetries of the action for scalar fields in d=2 dimensions are promoted to local gauge invariances of both chiralities. The complete action and transformation rules are given; both are infinitely nonlinear.

Quantum BRST charge for quadratically nonlinear lie algebras

We consider the construction of a nilpotent BRST charge for extensions of the Virasoro algebra of the form {Ta,Tb}=fabcTc+VabcdTcTd, (classical algebras in terms of Poisson brackets) and [Ta,Tb]=habI+fabcTc+Vabcd(TcTd)(quantum algebras in terms of commutator brackets; normal ordering of the product (TcTd) is understood). In both cases we assume that the set of generators {Ta} splits into a set {Hi} generating an ordinary Lie algebra and remaining generators {Sα}, such that only theVijαβ are nonvanishing. In the classical case a nilpotent BRST charge can always be constructed; for the quantum case we derive a condition which is necessary and sufficient for the existence of a nilpotent BRST charge. Non-trivial examples are the spin-3 algebra with central chargec=100 and theso(N)-extended superconformal algebras with levelS=−2(N−3).

Fine structure of the Bethe ansatz for the spin-1/2 Heisenberg XXX model

The authors analyse the Bethe ansatz equations for the two-particle sector of the spin 1/2 Heisenberg XXX model on a one-dimensional lattice of length N. They show that, beginning at a critical lattice length of N=21.86, new pairs of real solutions develop, whereas complex solutions start to disappear. The integers (that appear in the logarithmic form of the Bethe equations) of the new solutions do not fit into the conventional classification scheme. The total number of solutions in the two-particle sector remains unchanged and is in agreement with the claim that the SU(2) extended Bethe ansatz gives a complete set of 2N eigenstates.