Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter based on improved approximation schemes

We present Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter which are based on improved approximations schemes. The potential matrix elements have been adapted for isospin asymmetric nuclear matter in order to account for the proton-neutron mass splitting in a more consistent way. The proton properties are particularly sensitive to this adaption and its consequences, whereas the neutron properties remains almost unaffected in neutron rich matter. Although at present full Brueckner calculations are still too complex to apply to finite nuclei, these relativistic Brueckner results can be used as a guidance to construct a density dependent relativistic mean field theory, which can be applied to finite nuclei. It is found that an accurate reproduction of the Dirac-Brueckner-Hartree-Fock equation of state requires a renormalization of these coupling functions.Comment: 34 pages, 9 figures, submitted to Eur. Phys. J.

D-brane conformal field theory

We outline the structure of boundary conditions in conformal field theory. A boundary condition is specified by a consistent collection of reflection coefficients for bulk fields on the disk together with a choice of an automorphism \omega of the fusion rules that preserves conformal weights. Non-trivial automorphisms \omega correspond to D-brane configurations for arbitrary conformal field theories.Comment: 7 pages, LaTeX2e. Slightly extended version of a talk given by J. Fuchs at the 31st International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, Germany, September 199

Solitonic sectors, conformal boundary conditions and three-dimensional topological field theory

The correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary world sheets can be expressed in terms of Wilson graphs in appropriate three-manifolds. We present a systematic approach to boundary conditions that break bulk symmetries. It is based on the construction, by `alpha-induction', of a fusion ring for the boundary fields. Its structure constants are the annulus coefficients and its 6j-symbols give the OPE of boundary fields. Symmetry breaking boundary conditions correspond to solitonic sectors.Comment: 9 pages, LaTeX2e. Invited talk by Christoph Schweigert at the TMR conference ``Non-perturbative quantum effects 2000'', Paris, September 200

The action of outer automorphisms on bundles of chiral blocks

On the bundles of WZW chiral blocks over the moduli space of a punctured rational curve we construct isomorphisms that implement the action of outer automorphisms of the underlying affine Lie algebra. These bundle-isomorphisms respect the Knizhnik-Zamolodchikov connection and have finite order. When all primary fields are fixed points, the isomorphisms are endomorphisms; in this case, the bundle of chiral blocks is typically a reducible vector bundle. A conjecture for the trace of such endomorphisms is presented; the proposed relation generalizes the Verlinde formula. Our results have applications to conformal field theories based on non-simply connected groups and to the classification of boundary conditions in such theories.Comment: 46 pages, LaTeX2e. Final version (Commun.Math.Phys., in press). We have implemented the fact that the group of automorphisms in general acts only projectively on the chiral blocks and corrected some typo

A representation theoretic approach to the WZW Verlinde formula

By exploring the description of chiral blocks in terms of co-invariants, a derivation of the Verlinde formula for WZW models is obtained which is entirely based on the representation theory of affine Lie algebras. In contrast to existing proofs of the Verlinde formula, this approach works universally for all untwisted affine Lie algebras. As a by-product we obtain a homological interpretation of the Verlinde multiplicities as Euler characteristics of complexes built from invariant tensors of finite-dimensional simple Lie algebras. Our results can also be used to compute certain traces of automorphisms on the spaces of chiral blocks. Our argument is not rigorous; in its present form this paper will therefore not be submitted for publication.Comment: 37 pages, LaTeX2e. wrong statement in subsection 4.2 corrected and rest of the paper adapte