Simple Current Actions of Cyclic Groups

Permutation actions of simple currents on the primaries of a Rational Conformal Field Theory are considered in the framework of admissible weighted permutation actions. The solution of admissibility conditions is presented for cyclic quadratic groups: an irreducible WPA corresponds to each subgroup of the quadratic group. As a consequence, the primaries of a RCFT with an order n integral or half-integral spin simple current may be arranged into multiplets of length k^2 (where k is a divisor of n) or 3k^2 if the spin of the simple current is half-integral and k is odd.Comment: Added reference, minor change

Symmetry breaking boundaries II. More structures; examples

Various structural properties of the space of symmetry breaking boundary conditions that preserve an orbifold subalgebra are established. To each such boundary condition we associate its automorphism type. It is shown that correlation functions in the presence of such boundary conditions are expressible in terms of twisted boundary blocks which obey twisted Ward identities. The subset of boundary conditions that share the same automorphism type is controlled by a classifying algebra, whose structure constants are shown to be traces on spaces of chiral blocks. T-duality on boundary conditions is not a one-to-one map in general. These structures are illustrated in a number of examples. Several applications, including the construction of non-BPS boundary conditions in string theory, are exhibited.Comment: 51 pages, LaTeX2

Completeness of boundary conditions for the critical three-state Potts model

We show that the conformally invariant boundary conditions for the three-state Potts model are exhausted by the eight known solutions. Their structure is seen to be similar to the one in a free field theory that leads to the existence of D-branes in string theory. Specifically, the fixed and mixed boundary conditions correspond to Neumann conditions, while the free boundary condition and the new one recently found by Affleck et al [1] have a natural interpretation as Dirichlet conditions for a higher-spin current. The latter two conditions are governed by the Lee\hy Yang fusion rules. These results can be generalized to an infinite series of non-diagonal minimal models, and beyond.Comment: 9 pages, LaTeX2

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

ERTS orbit maintenance

Error drift in the ERTS orbit maintenance problem is determined from the actual ground trace errors that the spacecraft experienced over the first 3 1/2 repeat cycles. Actual data are fitted to a parametric model of ground trace error by a least squares method, and initial offsets to these key parameters as well as their rates of change are extrapolated forward analytically to obtain the future ground trace drift in orbital estimates

From Dynkin diagram symmetries to fixed point structures

Any automorphism of the Dynkin diagram of a symmetrizable Kac-Moody algebra induces an automorphism of the algebra and a mapping between its highest weight modules. For a large class of such Dynkin diagram automorphisms, we can describe various aspects of these maps in terms of another Kac-Moody algebra, the `orbit Lie algebra'. In particular, the generating function for the trace of the map on modules, the `twining character', is equal to a character of the orbit Lie algebra. Orbit Lie algebras and twining characters constitute a crucial step towards solving the fixed point resolution problem in conformal field theory.Comment: Latex, 60 pages (extended version 63 pages), 4 uuencoded figures Formula (6.25) corrected. While this correction might be important in applications of our work, the results of the paper are not affected by it. In the present submission the "extended version" is default. In this version the corrected formula is (6.32

A matrix S for all simple current extensions

A formula is presented for the modular transformation matrix S for any simple current extension of the chiral algebra of a conformal field theory. This provides in particular an algorithm for resolving arbitrary simple current fixed points, in such a way that the matrix S we obtain is unitary and symmetric and furnishes a modular group representation. The formalism works in principle for any conformal field theory. A crucial ingredient is a set of matrices S^J_{ab}, where J is a simple current and a and b are fixed points of J. We expect that these input matrices realize the modular group for the torus one-point functions of the simple currents. In the case of WZW-models these matrices can be identified with the S-matrices of the orbit Lie algebras that we introduced in a previous paper. As a special case of our conjecture we obtain the modular matrix S for WZW-theories based on group manifolds that are not simply connected, as well as for most coset models.Comment: Phyzzx, 53 pages 1 uuencoded figure Arrow in figure corrected; Forgotten acknowledment to funding organization added; DESY preprint-number adde

Ursell operators in statistical physics of dense systems: the role of high order operators and of exchange cycles

The purpose of this article is to discuss cluster expansions in dense quantum systems as well as their interconnection with exchange cycles. We show in general how the Ursell operators of order 3 or more contribute to an exponential which corresponds to a mean-field energy involving the second operator U2, instead of the potential itself as usual. In a first part, we consider classical statistical mechanics and recall the relation between the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles) and show that each Ursell operator Un with n greater or equal to 3 contains a ``tree-reducible part'', which groups naturally with U2 through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles, and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach, in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum statistics and dynamics.Comment: 31 pages, 7 figure