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.
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.
30074223
Operator-product coefficients in nondiagonal conformal field theories.
The problems involved in the determination of operator-product coefficients in nondiagonal conformal field theories are explained. The methods of Dotsenko and Fateev are used to derive formulas which allow one to compute these coefficients. A careful treatment of the issue of uniqueness of the results proves to be necessary
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.
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.
119087230
Logarithmic conformal field theories via logarithmic deformations
We construct logarithmic conformal field theories starting from an ordinary conformal field theory -- with a chiral algebra C and the corresponding space of states V -- via a two-step construction: ...
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.
