10470936
CFT fusion rules, DHR gauge groups and CAR algebras
It is demonstrated that several series of conformal field theories, while satisfying braid group statistics, can still be described in the conventional setting of the DHR theory, i.e. their superselection structure can be understood in terms of a compact DHR gauge group. Besides theories with only simple sectors, these include (the untwisted part of) c = 1 orbifold theories and level-two WZW theories. We also analyse the relation between these models and theories of complex free fermions.
120895757
The connections between Wess-Zumino-Witten models and free field theories
Abstract The relations between Wess-Zumino-Witten models and free field theories are reviewed. In particular the possibility of quantum equivalence between these two types of conformal field theories is investigated. Supersymmetric Wess-Zumino-Witten models are also discussed.
119511581
Conformal embeddings and hidden symmetries of free fermion theories
It is shown that the conformal field theory of free complex fermions transforming in the (anti)symmetric tensor representation R of u(N) is characterized by a nontrivial operator algebra. However, this theory can be naturally embedded into the theory of free Dirac fermions in the defining representation of u(dimR); the latter theory corresponds to an operator algebra which is trivial in the sense that e.g. φ×φ+ = 1. We argue that these observations can be generalized to any system of free fermions possessing an energy-momentum tensor of the Sugawara form. As a consequence, there exist no further cases where a free fermion theory is quantum equivalent to a WZW theory, besides the ones already well known (i.e. those based on the current algebras so(N) and u(N) with unit central charge).
119834629
The computation of the operator algebra in non-diagonal conformal field theories
The computation of the operator algebra in conformal field theories with Feigin-Fuks type correlation functions is described. The special features of non-diagonal theories are pointed out. Detailed formulae are provided for the {ital c}{lt}1 minimal series and for {ital A}{sub 1} WZW theories. As examples, the operator product coefficients for the {bold E}{sub 6}, {bold E}{sub 7}, and {bold D}{sub {ital l}} type {ital A}{sub 1} WZW theories are calculated. {copyright} 1989 Academic Press, Inc.
119750730
Level 1 WZW superselection sectors
AbstractThe superselection structure of the Wess-Zumino-Witten theory based on the affine Lie algebra
$$\widehat{so}(N)$$
 at level one is investigated for arbitraryN. By making use of the free fermion representation of the affine algebra, the endomorphisms which represent the superselection sectors on the observable algebra can be constructed as endomorphisms of the underlying Majorana algebra. These endomorphisms do not close on the chiral algebra of the theory, but we are able to obtain a larger algebra on which the endomorphisms close. The composition of equivalence classes of the endomorphisms reproduces the WZW fusion rules.
120441230
Nonrenormalizable field theories at finite temperature
We comment on the effects of finite temperature in two purely fermionic theories. While in the Nambu-Jona-Lasinio model a second order phase transition takes place, we find no phase transition in a model of composite gauge bosons.
118621064
Dirac fermions in graphene and analogues: magnetic field and topological properties
This is a short review of two-dimensional Dirac fermions in graphene and similar systems such as boron nitride, quasi-2D organic salts $\alpha$-(BEDT-TTF)$_2$I$_3$, artificial graphene with cold atoms in optical lattices, etc. The emphasis is on magnetic field properties (semi-classical quantization of cyclotron orbits, Landau levels, quantum Hall effect, magneto-plasmons, magneto-phonon resonance, magneto-transport, etc.) and on topological properties (Berry phase, winding number, inter-band effects, merging transition of Dirac points, etc.).
119325012
RCFT with defects: Factorization and fundamental world sheets
It is known that for any full rational conformal field theory, the correlation functions that are obtained by the TFT construction satisfy all locality, modular invariance and factorization conditi ...