121251376
Thermal and superthermal properties of supersymmetric field theories
Abstract We discuss the finite-temperature behaviour of supersymmetric field theories. We show that their “superthermal” properties which concern the question of susy breaking at finite temperature and their thermal properties must be considered separately. Susy breaking is determined by the so-called superthermal ensemble, whereas thermodynamical properties follow from the conventional thermal ensemble, leading to the usual statistics for the bosonic and fermionic components of a superfield. We show that superspace techniques can be used in a straightforward way only for superthermal Green functions but not for thermal ones. We also discuss the possibility of finite-temperature susy restoration and the implications of Goldstone's theorem at finite temperature.
118981675
Higher level WZW sectors from free fermions
We introduce a gauge group of internal symmetries of an ambient algebra as a new tool for investigating the superselection structure of WZW theories and the representation theory of the corresponding affine Lie algebras. The relevant ambient algebra arises from the description of these conformal field theories in terms of free fermions. As an illustration we analyze in detail the so(N) WZW theories at level two, which allows us in particular to construct explicit bases for the level-two irreducible highest weight modules. In this case there is actually a homomorphism from the representation ring of the gauge group to the subring of the WZW fusion ring that corresponds to the Neveu–Schwarz sector, even though the level-two observable algebra is smaller than the gauge invariant subalgebra of the field algebra.
116310735
Quantum symmetries in the algebraic description of WZW theories
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.
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 .
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.).
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.
