14139601
Fusion rules in conformal field theory
Several aspects of fusion rings and fusion rule algebras, and of their manifestations in two-dimensional (conformal) field theory, are described: diagonalization and the connection with modular invariance; the presentation in terms of quotients of polynomial rings; fusion graphs; various strategies that allow for a partial classification; and the role of the fusion rules in the conformal bootstrap programme.
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).
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 .
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.
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.
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.
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 ...
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.
