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.     

Strings fromN=2 gauged Wess-Zumino-Witten models

We present an algebraic approach to string theory. An embedding ofsl(2|1) in a super Lie algebra together with a grading on the Lie algebra determines a nilpotent subalgebra of the super Lie algebra. Chirally gauging this subalgebra in the corresponding Wess-Zumino-Witten model, breaks the affine symmetry of the Wess-Zumino-Witten model to some extension of theN=2 superconformal algebra. The extension is completely determined by thesl(2|1) embedding. The realization of the superconformal algebra is determined by the grading. For a particular choice of grading, one obtains in this way, after twisting, the BRST structure of a string theory. We classify all embeddings ofsl(2|1) into Lie super algebras and give a detailed account of the branching of the adjoint representation. This provides an exhaustive classification and characterization of both all extendedN=2 superconformal algebras and all string theories which can be obtained in this way.     

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.     

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.     

On the unitarity of gauged non-compact WZNW strings

In this paper we investigate the unitarity of gauged non-compact WZNW strings, i.e., string theories formulated as G/H^′$G/H^{\prime }$ WZNW models, where G   is a non-compact group. These models represent string theories on non-trivial curved space–times with one time-like component. We will prove that for the class of models connected to Hermitian symmetric spaces, and a natural set of discrete highest weight representations, the BRST formulation, in which the gauging is defined through a BRST condition, yields unitarity. Unitarity requires the level times the Dynkin index to be an integer, as well as integer valued highest weights w.r.t. the compact subalgebra. We will also show that the BRST formulation is not equivalent to the conventional GKO coset formulation, defined by imposing a highest weight condition w.r.t. H^′$H^{\prime }$. The latter leads to non-unitary physical string states. This is, to our knowledge, the first example of a fundamental difference between the two formulations.     

On the symplectic structure of general relativity

The relation between the symplectic structures on the canonical and radiative phase spaces of general relativity is exhibited.Alfred P. Sloan Research Fellow. Supported in part by the NSF contract PHY80-08155 and by a grant from the Syracuse University Research and Equipment FundSupported in part by crédits ministériels, tranche spéciale     

On hvLif -like solutions in gauged Supergravity

We perform a thorough investigation of Lifshitz-like metrics with hyperscaling violation (hvLif) in four-dimensional theories of gravity coupled to an arbitrary number of scalars and vector fields, obtaining new solutions, electric, magnetic, and dyonic, that include the known ones as particular cases. After establishing some general results on the properties of purely hvLif solutions, we apply the previous formalism to the case of ${\mathcal {N}}=2,~d=4$ supergravity in the presence of Fayet–Iliopoulos terms, obtaining particular solutions to the $t^3$ -model, and explicitly embedding some of them in Type-IIB string theory.     

On algebraic equations satisfied by correlators in Wess-Zumino-Witten models

Apart from the Knizhnik-Zamolodchikov differential equations, correlation functions in Wess-Zumino-Witten models of conformal field theory satisfy a certain system of algebraic equations. We show that hypergeometric solutions of KZ equations constructed in [3] do satisfy these algebraic equations.     

On the unitarity of gauged non-compact world-sheet supersymmetric WZNW models

In this paper we generalize our investigation of the unitarity of non-compact WZNW models connected to Hermitian symmetric spaces to the N=1$N=1$ world-sheet supersymmetric extension of these models. We will prove that these models have a unitary spectrum in a BRST approach for antidominant highest weight representations if the level and weights of the gauged subalgebra are integers. We will find new critical string theories in 7 and 9 space–time dimensions.     

Dimensional regularization in the Wess-Zumino-Witten model

A method is described for the dimensional regularization and renormalization of a two-dimensional non-linear sigma model with torsion, the Wess-Zumino-Witten model. The technique solves the problems generated by the presence of the antisymmetric tensor e^uv. The two-loop calculation agrees with the non-perturbative result.     

Three-loop beta-function of the Wess-Zumino-Witten model

The three-loop beta function for the Wess-Zumino-Witten model is presented. Dimensional regularization is used in the calculation. The result agrees with the exact solution.     

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.     

On the general structure of nonlinear equations integrable by the general linear spectral problem

Two beams of indistinguishable fermions from independent sources cannot produce an interference pattern that changes when the wavefunction of each single-fermion state for one beam is multiplied by — 1; they cannot produce interference the way photons from independent sources can. This means the changes in neutron interference caused by a magnetic field applied to one of the beams cannot be interpreted as equivalent to changes that could be made by rotating the source of one beam by 2π radians. If it is assumed that rotation by 2π radians cannot be observed, the argument made here becomes a simple proof that particles with half-integral spin cannot be bosons.