Global aspects of gauged Wess-Zumino-Witten models

A study of the gauged Wess-Zumino-Witten models is given focusing on the effect of topologically non-trivial configurations of gauge fields. A correlation function is expressed as an integral over a moduli space of holomorphic bundles with quasi-parabolic structure. Two actions of the fundamental group of the gauge group is defined: One on the space of gauge invariant local fields and the other on the moduli spaces. Applying these in the integral expression, we obtain a certain identity which relates correlation functions for configurations of different topologies. It gives an important information on the topological sum for the partition and correlation functions.     

On the general structure of gauged Wess-Zumino-Witten terms

The problem of gauging a closed form is considered. When the target manifold is a simple Lie group G, it is seen that there is no obstruction to the gauging of a subgroup H ∋ G if we may construct from the form a cocycle for the relative Lie algebra cohomology (or for the equivariant cohomology), and an explicit general expression for these cocycles is given. The common geometrical structure of the gauged closed forms and the D'Hoker and Weinberg effective actions of WZW type, as well as the obstructions for their existence, is also exhibited and explained.     

Gauss law commutator in the chirally gauged Wess-Zumino-Witten model

We evaluate the commutator of the Gauss law constraints starting from the chirally gauged Wess-Zumino-Witten action. The calculations are done at tree level, i.e. by evaluating corresponding Poisson brackets. The results are compared with commutators obtained by others directly from the gauged fermionic theory, and with Faddeev's results based on cohomology.     

The Ka -Moody anomaly. An obstruction to a gauged Wess-Zumino-Witten model

We present a gauged Wess-Zumino-Witten model, in which the topological term is a difference of Chern-Simons forms. Part of the Ka -Moody currents become first-class constraints, thus generating local Ka -Moody symmetries. This model provides a lagrangian relization of the Goddard-Kent-Olive coset construction. At the quantum level, however, the Ka -Moody anomaly vanishes only for a negative value of the central charge k.     

The spectrum of Wess-Zumino-Witten models

We consider the SU(2) and SO(3) Wess-Zumino-Witten models in the Schrödinger representation. Wave functions are sections of a line bundle over a loop group. We compute the spectrum of irreducible lowest weight representations appearing in the model. Fusion rules of the operator product expansion are also discussed.     

Light-Cone Gauge for N = 2 Strings

Covariant quantization of self-dual strings in 2 + 2 flat dimensions reduces them to their zero modes, a consequence of extended world-sheet supersymmetry. We demonstrate how to arrive at the same result more directly by employing a double light-cone gauge. An unconventional feature of this gauge is the removal of anticommuting degrees of freedom by commuting symmetries and vice versa. The reducibility of the N = 4 string and its equivalence with the N = 2 string become apparent.     

On the Wess-Zumino-Witten models on Riemann surfaces

We give a formulation of the Wess-Zumino-Witten models on Riemann surfaces of arbitrary genus in which the Ward identities for the current algebras become complete. It requires twisting the models in a non-abelian way by Lie group elements. The Ward identities are written in terms of twisted Poincaré series for Schottky groups and the zero modes of the currents are defined by a Lie derivation acting on the twists. Furthermore, we identify the denominator of the chiral partition function and we argue that both the numerator and the denominator of the partition function satisfy a heat equation on the moduli space.     

Anti-de Sitter BPS black holes in N=2 gauged supergravity

Electrically charged solutions breaking half of the supersymmetry in Anti-de Sitter four dimensional N=2 supergravity coupled to vector supermultiplets are constructed. These static black holes live in an asymptotic AdS₄ space time. The Killing spinor, i.e., the spinor for supersymmetry variation is explicitly constructed for these solutions.     

Spectra of Wess-Zumino-Witten models with arbitrary simple groups

We consider the Wess-Zumino-Witten two-dimensional sigma models with fields taking values in an arbitrary connected (but not necessarily simply connected) simple Lie groupG. The quantum states of the theory are realized geometrically as sections of a line bundle over the loop groupLG. The action of the current algebra of the theory is decomposed into highest weight representations by explicit construction of the highest weight states. This solves for the spectrum of the models. As a by-product, we obtain modular invariant partition functions of the theory on tori. The present paper extends the results of [7] where the casesG=SU(2) andSO(3) were treated.Ce rapport a été publié en partie grâce à une subvention du Fonds FCAR pour l'aide et le soutien à la rercherche     

Strings and D=4

It is argued that the unique infrared behaviour of non-abelian gauge couplings in four dimensions could be responsible, in closed super- (or heterotic) string theory, for dynamical supersymmetry breaking and for compactification to D=4 with string-scale compactified radii.     

Super-Toda theories and W-algebras from superspace Wess-Zumino-Witten models

Using a superspace approach, it is proved that aN=1 Super-Toda theory can be seen as a constrained WZW model based on a supergroup. The gauge transformations which survive the constraints are then usedà la Drinfeld Sokolov to determine explicity the super-W algebra underlying this theory. The conformal spin content of any such super-Walgebra is provided in the general case.URA 14-36 du CNRS, associée à l'E.N.S. de Lyon, et au L.A.P.P.     

Bogomolny-type equations for gravitating gauged sigma models

It is shown that the complete set of field equations of a gauged sigma model coupled to gravity is satisfied by a set of first-order equations when the metric is static.     

Supersymmetric preon models with gauged colour-flavour symmetry

We have conducted a search for globally supersymmetric preon models with gauged colour-flavour symmetries. Theories with both two- and three-preon composites, and colour-flavour groups from E₆ down to the standard model, are examined under the following conditions: asymptotically-free metacolour, anomaly-free gauged symmetries, and Pauli principle obeyed. It is found that there are no models with three or more supersymmetric families. If supersymmetry is broken, one model with four families emerges. The purely fermionic preon theories can also be considered as the light sector of a chiral supersymmetric theory, with supersymmetry breaking at the preon level.