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

Galois Modular Invariants of WZW Models

The set of modular invariants that can be obtained from Galois transformations is investigated systematically for WZW models. It is shown that a large subset of Galois modular invariants coincides with simple current invariants. For algebras of type B and D infinite series of previously unknown exceptional automorphism invariants are found.Comment: phyzzx macros, 38 pages. NIKHEF-H/94-3

Twining characters, orbit Lie algebras, and fixed point resolution

We describe the resolution of field identification fixed points in coset conformal field theories in terms of representation spaces of the coset chiral algebra. A necessary ingredient from the representation theory of Kac Moody algebras is the recently developed theory of twining characters and orbit Lie algebras, as applied to automorphisms representing identification currents.Comment: Latex, 24 pages. Slightly extended version of lectures by J. Fuchs at a workshop in Razlog (Bulgaria) in August 199

Quasi-Galois Symmetries of the Modular S-Matrix

The recently introduced Galois symmetries of RCFT are generalized, for the WZW case, to `quasi-Galois symmetries'. These symmetries can be used to derive a large number of equalities and sum rules for entries of the modular matrix S, including some that previously had been observed empirically. In addition, quasi-Galois symmetries allow to construct modular invariants and to relate S-matrices as well as modular invariants at different levels. They also lead us to an extremely plausible conjecture for the branching rules of the conformal embeddings of g into so(dim g).Comment: 20 pages (A4), LaTe

Superconformal Coset Equivalence from Level-Rank Duality

We construct a one-to-one map between the primary fields of the N=2 superconformal Kazama-Suzuki models G(m,n,k) and G(k,n,m) based on complex Grassmannian cosets, using level-rank duality of Wess-Zumino-Witten models. We then show that conformal weights, superconformal U(1) charges, modular transformation matrices, and fusion rules are preserved under this map, providing strong evidence for the equivalence of these coset models.Comment: 25 pages, harvmac, no figures, added referenc

Implications of an arithmetical symmetry of the commutant for modular invariants

We point out the existence of an arithmetical symmetry for the commutant of the modular matrices S and T. This symmetry holds for all affine simple Lie algebras at all levels and implies the equality of certain coefficients in any modular invariant. Particularizing to SU(3)_k, we classify the modular invariant partition functions when k+3 is an integer coprime with 6 and when it is a power of either 2 or 3. Our results imply that no detailed knowledge of the commutant is needed to undertake a classification of all modular invariants.Comment: 17 pages, plain TeX, DIAS-STP-92-2

Twining characters and orbit Lie algebras

We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary characters of some other generalized Kac-Moody algebra, the so-called orbit Lie algebra. Some applications to problems in conformal field theory, algebraic geometry and the theory of sporadic simple groups are sketched.Comment: 6 pages, LaTeX, Talk given by C. Schweigert at the XXI international colloquium on group theoretical methods in physics, July 1996, Goslar, German

Significance of interface anisotropy in laser induced magnetization precession in ferromagnetic metal films

Laser induced ultrafast demagnetization in ferromagnetic metals was discovered almost 20 years ago, but currently there is still lack of consensus on the microscopic mechanism responsible for the corresponding transfer of angular momentum and energy between electron, lattice and spin subsystems. A distinct, but intrinsically correlated phenomenon occurring on a longer timescale is the magnetization precession after the ultrafast demagnetization process, if a magnetic field is applied to tilt the magnetization vector away from its easy direction, which can be attributed to the change of anisotropy after laser heating. In an in-plane magnetized Pt/Co/Pt thin film with perpendicular interface anisotropy, we found excellent agreement between theoretical prediction with plausible parameters and experimental data measured using time resolved magneto-optical Kerr effect. This agreement confirms that the time evolution of the anisotropy field, which is driven by the interaction between electrons and phonons, determines the magnetization precession completely. A detailed analysis shows that, even though the whole sample is magnetized in-plane, the dynamic interface anisotropy field dictates the initial phase of the magnetization precession, highlighting the significance of the interface anisotropy field in laser induced magnetization precession.Comment: 11 pages, 2 figure

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