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.
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.
121181228
WZW fusion rules, quantum groups, and the modular matrix S
A simple algorithm, due to Walton, for calculating the fusion rules of WZW theories is proved and applied to several nontrivial examples. The results are used to gain new insight in the structure of non-fully reducible modules of the quantum groups Uqg, and to find the explicit form of the modular transformation matrix S for some cases where it had not yet been worked out before.
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.
121995098
On the connection between WZW and free field theories
Abstract A large class of primary fields which appear at any level of the WZW theories (of types A N , B N , C N , D N , E 6 , and E 7 ) are shown to posses simple power-like four-point functions. As a consequence, these fields, which are in 1-1 correspondence with the center of the covering group, may be written as symmetrized products of level one fields. The latter are known to be related to free fermions (A N , B N , D N ) or free bosons (A N , D N , E 6 , E 7 ). Our results indicate that a relation to free field theory exists also for the case of C N .
118685069
Klein tunneling in graphene: optics with massless electrons
Abstract
This article provides a pedagogical review on Klein tunneling in graphene, i.e. the
peculiar tunneling properties of two-dimensional massless Dirac electrons. We consider two
simple situations in detail: a massless Dirac electron incident either on a potential step
or on a potential barrier and use elementary quantum wave mechanics to obtain the
transmission probability. We emphasize the connection to related phenomena in optics, such
as the Snell-Descartes law of refraction, total internal reflection, Fabry-Pérot
resonances, negative refraction index materials (the so called meta-materials), etc. We
also stress that Klein tunneling is not a genuine quantum tunneling effect as it does not
necessarily involve passing through a classically forbidden region via evanescent waves. A
crucial role in Klein tunneling is played by the conservation of (sublattice) pseudo-spin,
which is discussed in detail. A major consequence is the absence of backscattering at
normal incidence, of which we give a new shorten proof. The current experimental status is
also thoroughly reviewed. The Appendix contains the discussion of a one-dimensional toy
model that clearly illustrates the difference in Klein tunneling between mono- and
bi-layer graphene.

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 ...